How to find an angle with cosine - ACT Math
Card 0 of 7
In the above triangle, 
and 
. Find 
.
In the above triangle,
With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the adjacent and hypotenuse sides of the triangle with relation to the angle. With this information, we can use the cosine function to find the angle.
With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the adjacent and hypotenuse sides of the triangle with relation to the angle. With this information, we can use the cosine function to find the angle.
Compare your answer with the correct one above
For the above triangle, 
and 
. Find 
.
For the above triangle,
With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the adjacent and hypotenuse sides of the triangle with relation to the angle. With this information, we can use the cosine function to find the angle.
With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the adjacent and hypotenuse sides of the triangle with relation to the angle. With this information, we can use the cosine function to find the angle.
Compare your answer with the correct one above
For the above triangle, 
and 
. Find 
.
For the above triangle,
With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the adjacent and hypotenuse sides of the triangle with relation to the angle. However, if we plug the given values into the formula for cosine, we get:
This problem does not have a solution. The sides of a right triangle must be shorter than the hypotenuse. A triangle with a side longer than the hypotenuse cannot exist. Similarly, the domain of the arccos function is 
. It is not defined at 1.3.
With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the adjacent and hypotenuse sides of the triangle with relation to the angle. However, if we plug the given values into the formula for cosine, we get:
This problem does not have a solution. The sides of a right triangle must be shorter than the hypotenuse. A triangle with a side longer than the hypotenuse cannot exist. Similarly, the domain of the arccos function is
Compare your answer with the correct one above
A 
rope is thrown down from a building to the ground and tied up at a distance of 
from the base of the building. What is the angle measure between the rope and the ground? Round to the nearest hundredth of a degree_._
A
You can draw your scenario using the following right triangle:
Recall that the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse of the triangle. You can solve for the angle by using an inverse cosine function:
or 
degrees.
You can draw your scenario using the following right triangle:
Recall that the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse of the triangle. You can solve for the angle by using an inverse cosine function:
Compare your answer with the correct one above
What is the value of 
in the right triangle above? Round to the nearest hundredth of a degree.
What is the value of
Recall that the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse of the triangle. You can solve for the angle by using an inverse cosine function:
or 
.
Recall that the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse of the triangle. You can solve for the angle by using an inverse cosine function:
Compare your answer with the correct one above
A support beam (buttress) lies against a building under construction. If the beam is 
feet long and strikes the building at a point 
feet up the wall, what angle does the beam strike the building at? Round to the nearest degree.
A support beam (buttress) lies against a building under construction. If the beam is
Our answer lies in inverse functions. If the buttress is 
feet long and is 
feet up the ladder at the desired angle, then:
Thus, using inverse functions we can say that 
Thus, our buttress strikes the buliding at approximately a 
angle.
Our answer lies in inverse functions. If the buttress is
Thus, using inverse functions we can say that
Thus, our buttress strikes the buliding at approximately a
Compare your answer with the correct one above
A stone monument stands as a tourist attraction. A tourist wants to catch the sun at just the right angle to "sit" on top of the pillar. The tourist lies down on the ground 
meters away from the monument, points the camera at the top of the monument, and the camera's display reads "DISTANCE -- 
METERS". To the nearest 
degree, what angle is the sun at relative to the horizon?
A stone monument stands as a tourist attraction. A tourist wants to catch the sun at just the right angle to "sit" on top of the pillar. The tourist lies down on the ground
Our answer lies in inverse functions. If the monument is 
meters away and the camera is 
meters from the monument's top at the desired angle, then:
Thus, using inverse functions we can say that 
Thus, our buttress strikes the buliding at approximately a 
angle.
Our answer lies in inverse functions. If the monument is
Thus, using inverse functions we can say that
Thus, our buttress strikes the buliding at approximately a
Compare your answer with the correct one above