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Real World Trig
Problems
Problems
Trig Ratios
Other world problems
Pythagorean triplets
100
Who made Pythagoras Theorem
Pythagoras of Samos
100
A 75-foot building casts an 82-foot shadow. What is the angle of elevation of the sun?
It's going to use an inverse tan, since we are looking for an angle, and we have oppisite and adjacent.
tan-1(75/82)
100
What is the value of X?
X is 22.9ft.
,since you are using tangent, so you will use 2/X, since x is the adjacent. Then we divide 2 by tan(5) to get your answer.
100
A rocket is ascending from a launchpad. When the rocket is 2000 meters directly above the ground, the straight-line distance from the observation bunker (on the ground) to the rocket is 5000 meters. What is the angle of elevation from the bunker to the rocket?
We will be using sine, since we have the opposite (2000), and the hypotenuse (5000). so we do sin-1 (2000/5000), giving us the angle of 23.6o.
100
If I have 3 and 4 what would the third number be for a triplet?
5
3^2 = 9
4^2 = 16
________________
9 + 16 = 25
_________
5^2 = 25
5 is a match!
200
What is Pythagoras theorem
a2+b2=c2
Side square Plus Side square equals big square.
200
15-ft ramp is up 3 feet from the ground, what's the angle of inclination?
11.5o
Explanation - The hypotenuse is the ramp length, how far up the ramp is the opposite length, so weuse sine-1 (3/15), which is the inverse of sine.
200
What is the angle of x? (Round up to the nearest whole number.)
The angle is 37o
1.)We are using tan, since we have the opposite and the adjacent.
2.) We use the operation tan-1 (or inverse tan) (23 (oppisite)/31(adjacent)) and we get 37.
200
A 50-meter cable is attached to the top of a deflector shield generator. The cable forms a 65o angle with the ground. How far from the base of the generator is the cable anchored?
cos(65o) = X/50
multiply both sides by 50
x = 21.3 meters
200
If I have 5 and 12 what would the third number be for a triplet?
5^2 = 25
12^2 = 144
____________
25+144 = 139
________________
13^2 = 139
13 is a match!
300
What Kind of view is an angle of elevation
It is from the bottom to up
300
Problem: A wheelchair ramp needs to rise to a height of 1 meter over a horizontal distance of 5 meters. What is the angle of elvation of the ramp.
The answer is 11.31o, since we are using tan, because we have adjacent, and the opposite, 1 and 5 respectively.
300
A Hermes 450 drone is flying at a constant altitude of 800 meters. The operator spots a target at an angle of depression of 35o.
Question: What is the direct line-of-sight distance (slant range) from the drone to the target?
First you will use sin(), since it is the opposite and we have the hypotenuse (800/x). Then you divide both sides by sin(35o), since you will cancel out the x.
x = 1,394.8
300
An explorer on a new planet spots a crystalline tower. Standing 100 meters from the base, the angle of elevation to the top of the tower is 38o. How tall is the tower?
We are going to be using tan, since we are looking for the opposite, with the provided side being the adjacent. So we have the equation tan(38) = x/100
So we multiply both sides by 100, so 100* tan(38), and we get 78.13 meters.
300
If I have 20 as one of the sides, and 29 as the hypotenuse, what would the other side be to make it a triplet?
29^2 = 841
20^2 = 400
___________
841 - 400 = 441
√441 = 21
21 is a match!
400
What are the values of the sides of the 45o 45o , and the 30o, 60o triangles?
45 is 1, 1, square root 2.
30 is 1, 60 is square root 3, and 90 is 2
400
What is the angle of a right triangle with a height of 67 units, and 41 units.
59o, we get this by doing tan(67,41) since 67 is the opposite, and 41 is the height.
400
A mortar team must hit a target behind a wall. They need to launch at an angle where the projectile travels 500 meters forward while rising 300 meters, forming a right triangle with the launch point and the zenith.
We are going to be using inverse tan, since we have the adjacent, and the opposite given to us already. Which is 300, and 500 respectively.
After tan-1 (300/500) we get
x = 30.96.
since the x is in the tan function.
400
In the peaceful Elysian Fields, a statue of a hero stands on a pedestal. A beam of light from the underworld sun (dimly lit) strikes the statue, creating a 20-foot long shadow on the ground. If the angle of elevation to the top of the statue from the tip of the shadow is 30, how high is the statue?
What we are looking for is the opposite side of the triangle, so we are going to be using Tangent, so we have the equation tan(30o) = h/20, so we simply multiply both sides by 20 to get 11.55 ft.
400
If I have 48 as one of the sides and 73 as the hypotenuse, what would the other side be to make it a triplet?
73 ^ 2 = 5329
48^2 = 2304
____________
5329 - 2304 = 5025
__________________
√5025 = 55
55 is a match!
500
What is this Greek letter?
Theta - It's used to represent the measure of an acute angle in a right triangle.
500
From a hot-air balloon, Justin measures a 34 degrees∘ angle of depression to a landmark that's 1424 feet away, measuring horizontally. What's the balloon's vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
tan = opposite / adjacent
tan(34) = v/1424
vertical distance = 1424 * tan(24) = 960.5
V = 960.5
500
A roof truss is built with a total span of 30 feet. The rafters on each side are 17 feet long. Find the angle of inclination (pitch) of the roof.
First,we have an isosceles triangle, so we divide it in half, so that we can have two right triangles. We will be using cos, since we have the adjacent, and the hypotenuse. We are going to use cos-1(15/17), we end up getting 28.07o.
500
In a cyberpunk dimension, you are trying to aim a data-thief laser from the top of a skyscraper that is 320 meters tall, to a receiver on a hover-train that is 180 meters horizontally, what angle must the laser be?
First we need to find the hypotenuse, we do this by using pythagoras theorem, 320^2+180^2=c^2.
This gives us 367.15 meters.
Now that we have this, we are going to use inverse tangent to find the angle. You can use tan-1 (320/180) or you can use to get the angle 60.6o.
500
You have found the
Daily Double!
If you get the question right, you get double the points, if you get it wrong, you lose double the points
Missing side length in 27^2 +x = 45^2
The answer is 36 since we subtract both sides by 27^2 we get 1296 sqrt it we get 36.
We can double check by adding 27^2 and 36^2 to get 2025, square root it to get 45.