Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:

 or .

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.

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.

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.

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 .

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 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.

Cosine A = Adjacent / Hypotenuse = AB / AC = AB / 4

Cosine A = AB / 4

Cos (30º) = √3 / 2 = AB / 4

Solve for AB

√3 / 2 = AB / 4

AB = 4 * (√3 / 2) = 2√3

To solve this problem you need to make the triangle that the problem is talking about. Cosine is equal to the adjacent side over the hypotenuse of a right triangle 

So this is what our triangle looks like:

Now use the pythagorean theorem to find the other side: 

Sine is equal to the opposite side over the hypotenuse, the opposite side is 12