Special Right Triangles
Trig Ratios
Missing Sides and Angles
Trig Word Problems
Miscellaneous
100
Find the value of each variable.
x=9sqrt2
y=9
100
Express sin(E) as a fraction.
sin(E) = 2/9
100
Find the value of x. Round to the thousandths place.
x≈ 3.346
100
A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. The angle of elevation to the beacon is 7°. What is the ship’s horizontal distance from the lighthouse? Round to the nearest thousandth.
920.311 ft
100
What is the length of the side adjacent to theta ?
10 units
200
Find the value of each variable.
a = 8
b=4sqrt3
200
Express cos(Y) as a fraction in simplest terms.
cos(Y) = 3/5
200
Find the value of alpha . Round to the thousandths place.
alpha≈ 43.983^\circ
200
Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees. Is this a safe ramp? Show or explain your reasoning.
No, because the ramp angle is 11.310 degrees, which is more than 8.5 degrees.
200
Find the value of x. Round to the thousandths place.
x≈ 3.606
300
Find the length of segment SU.
15sqrt3 units
300
Express sin(A), cos(A), and tan(A) as a decimal. Round to the thousandths place if necessary.
sin(A)≈ 0.923
cos(A)≈ 0.385
tan(A)= 2.4
300
Find the measure of angles Q and O. Round to the thousandths place.
m\angleQ≈ 41.186°
m\angleO≈ 48.814°
300
Layla leans a 26-foot ladder against a wall so that it forms an angle of 61° with the ground. How high up the wall does the ladder reach? Round to the nearest thousandth.
22.740 ft
300
Explain how you know these right triangles are similar.
The triangles are similar by Angle-Angle Triangle Similarity Theorem since they have two pairs of congruent angles.
400
Find the area of triangle XYZ.
25sqrt3 units2
400
List two ratios of side lengths that are equal to tan(C) .
tan(C)={DE}/{EC}
tan(C)={BA}/{AC}
400
Find the value of each variable. Round to the thousandths place.
a≈ 1.928
b≈ 2.298
theta=50^\circ
400
If a tree has a height of 68 feet, what would be the angle of elevation from level ground measured from 78 feet away? Round to the nearest thousandth.
41.082°
400
Write a ratio equivalent to c/a .
e/f
500
Find x and y. Express lengths in simplest radical form with a rational denominator if necessary.
x=6
y=2sqrt3
500
Select all the true equations.
B, C, E
500
Find the value of each variable. Round to the thousandths place.
c≈ 9.849
theta≈ 23.962^{\circ}
beta≈ 66.038^\circ
500
From her eye, which stands 1.74 meters above the ground, Jada measures the angle of elevation to the top of a prominent skyscraper to be 51°. If she is standing at a horizontal distance of 148 meters from the base of the skyscraper, what is the height of the skyscraper? Round to the nearest thousandth.
184.505 m
500
Determine the value of theta that satisfies the equation. Explain your answer.
sin(28^\circ)=cos(theta)
theta=62 ^circ because the sine and cosine of complementary angles are equal.