Special Right Triangles
Pythagorean Theorem
Right Triangles
Unknown Parts of a Right Triangle
Finding Trig Ratios
100
One leg of a 45-45-90 triangle measures 2. What is the lengths of the other two sides?
2 and 2 square roots of 2
100
The two legs of a right triangle are 3 and 4. What is the hypotenuse?
5
100
One of the angles in a right triangle is 35 degrees. What is the measures of the other two angles?
90 and 55 degrees
100
What is the acronym to help remember the trig ratios?
SOH CAH TOA
sin(x)=opp/hyp
cos(x)=adj/hyp
tan(x)=opp/adj
100
In right triangle AOH, AO= 4; OH = 3; AH = 5. What is the Sine ratio of angle H?
4/5
200
The short leg of a 30-60-90 triangle measures 4. What is the length of the other sides?
8 and 4 square roots of 3
200
Would the following measures create a right triangle?
9, 12, 15
Yes
200
To solve for the measures of a right triangle means to find the measures of all its ________ and ___________.
angles, sides
200
Right triangle ABC: leg AB=18 leg BC=12. Find angle A.
33.7
200
In right triangle AOH, AO = 6; OH = 4; AH = square root of 52. What is the the measure of angle A?
m<A=33.7 degrees
300
The hypotenuse on a 45-45-90 triangle measures 6. What is the length of the legs?
3 square roots of 2
300
The hypotenuse of a right triangle is 5 and one of the legs is 2. What is the length of the other leg?
square root of 21
300
What is the longest side of a right triangle called?
Hypotenuse
Not the hippopotamus
300
Right triangle KLM: Angle M=40, Hypotenuse=8, Angle L=90. Find KL.
5.1
300
You are standing on a footbridge in a city park that is 12 feet high above a pond. You look down and see a duck in the water 7 feet away from the footbridge. What is the angle of depression (looking from the top of the bridge down to the duck).
59.7 degrees
400
The long leg of a 30-60-90 triangle measures 9. what is the length of the other two sides?
3 square roots of 3 and 6 square roots of 3
400
The length of two sides of a right triangle are both 8. What is the measure of the last side?
8 square roots of 2
400
Explain how to tell which side is adjacent to an angle.
It the side "next" to the angle, but is not the hypotenuse.
Maybe More Precise:
The adjacent side of a an acute angle in a triangle is the side that intersects the vertex to "create" the angle which is NOT the hypotenuse
400
Right triangle RST: Angle R=50, Angle S=90, ST=15. Find the missing angle and the hypotenuse RT.
Angle S=40 and RT=19.6
400
A soccer ball is placed 10 feet away from the goal, which is 8 feet high. You kick the ball and it hits the crossbar along the top of the goal. What is the angle of elevation of your kick?
38.7 degrees
500
The hypotenuse of a 30-60-90 triangle measures 10 square roots of 3. What are the lengths of the other two sides?
5 square roots of 3 and 15
500
The hypotenuse of a triangle measures 5 square roots of 2 and one leg measures 4. What is the length of the other leg?
Square root of 34
500
Describe how to find the opposite side of an angle.
It is the side of the triangle that does not intersect the vertex of the angle.
500
Right Triangle GHJ: Hypotenuse GJ=16, and leg GH=14. Find HJ, angle G and angle J.
angle G=29, angle J=61, HJ=7.7
500
When do you use the trigonometric ratio to find a side length of a right triangle and when to use the Pythagorean Theorem? Explain.
Pythagorean Theorem: Can be used in ANY right triangle when two sides are known to determine the missing third side length.
PT need to know: 2 sides; given right triangle
Trig Ratios: Can be used when given 1 side length and the angle opposite/adjacent to that side which is not the hypotenuse
Trig Ratios need to know: 1 side 1 angle; given right triangle