Right Triangle Basics
In a right triangle, what is the side opposite the 90° angle called?
Hypotenuse
In a right triangle, the opposite side is 4 and the hypotenuse is 5.
Find sin(θ).
4/5
In a 45°–45°–90° triangle, one leg is 8.
Find the hypotenuse.
8 root 2
If tan(θ) = 1, what is θ?
45 degrees
A ladder leans against a wall forming a 60° angle with the ground. Which trig function would you use to find the height of the wall if you know the ladder length?
sine
If a right triangle has legs of 3 and 4, what is the hypotenuse?
5
If opposite = 5 and hypotenuse = 13, what is sin(θ)?
5/13
In a 45°–45°–90° triangle, if a leg is 5, what is the hypotenuse?
5 root 2
If sin(θ) = 0.5, what is θ?
30 degrees
Find the area of a triangle that has 2 sides of lenghts 4 and 10 and the included angles is 30 degrees.
Final Answer:
The area of the triangle is 101010 square units.
In a right triangle, if the hypotenuse is 10 and one leg is 6, find the other leg.
8
ABC is a right triangle
AB=7cm, angle ABC=90degrees and angle ACB=64 degrees
Calculate the length of BC
BC≈3.4 cm
In a 30°–60°–90° triangle, the short leg is 5.
Find the hypotenuse.
Short leg × 2
5(2)=10
Terminal side of an angle passes through the point (5,-2). Find the cosine of the angle.
5 sqrt 29/29
How many triangles can be constructed with the following information:
a=2
b=4
angle A= 22
2
Name 3 Pythagorean triples
3,4,5
5,12,13
8, 15, 17
others may apply
Triangle ABC is a right triangle.
AC=12cm
∠ABC=90∘
∠ACB=35∘
Calculate the length of BC.
BC≈9.8 cm
In a 30°–60°–90° triangle, the hypotenuse is 14.
Find the long leg.
7 root 3
If
sin(θ)=sqrt3/2
find all possible angles between 0 degrees and 360 degrees
60° and 120°
(Remember sine is positive in Quadrants I and II.)
A tree is 20 m tall. The angle of elevation from the ground is 30°. How far away are you from the tree?
34.6 m
A 13ft ladder is leaning against the house. The top of the ladder touches the house at 10ft above the ground. How far away is the bottom of the ladder from the house?
The answer is
x= sqrt69
x≈8.3 ft
The perimeter of a right triangle is 24cm. The length of one of the sides is 10cm, the length of the other side is 8 cm. Calculate the size of the smallest angle of this triangle.
θ=sin-1(0.6)
θ≈36.87degrees
A square has side length 10. A diagonal is drawn across the square.
Find the length of the diagonal.
10sqrt2
The diagonal creates a 45°–45°–90° triangle.
d2=102+102
d2 = 200
d=10sqrt2
Find the area of a regular hexagon inscribed in a circle of radius 10.
A=150 sqrt 3
A ramp rises 3 meters over a horizontal distance of 4 meters. What is the angle of elevation?
36.9°