Question Type 2: Using SOH CAH TOA to find the angle given two sides Exercises

A support cable is $7\text{ m}$ long and makes an angle $x$ against the ground, raising the attachment point $4\text{ m}$ above the ground. Find $x$ in degrees to the nearest tenth.

Find the angle $\psi$ such that $\cos\psi=\dfrac{4}{7}$, giving your answer in degrees to two decimal places.

In right triangle $ABC$ with right angle at $C$, the hypotenuse $AB=7$ and the side $BC=4$ is opposite angle $A$. Find angle $A$ in degrees to the nearest whole number.

A ramp is 7 ft long and rises vertically by 4 ft. Calculate the incline angle $\beta$ between the ramp and the horizontal, to the nearest tenth of a degree.

A playground slide is $7 \text{ m}$ long and drops vertically by $4 \text{ m}$. At what angle $\gamma$ is the slide inclined relative to the horizontal? Give your answer to the nearest degree.

An observer measures the line of sight to a drone at $7 \text{ km}$ and notes its altitude is $4 \text{ km}$. Find the angle of elevation $\delta$ in degrees, to one decimal place.

Determine the angle $\omega$ satisfying $\tan\omega=\dfrac{4}{7}$, in degrees to the nearest tenth.

Find the angle $\theta$ (in degrees) such that $\sin\theta=\dfrac{4}{7}$.

A ladder of length 7 m leans against a vertical wall and reaches a height of 4 m up the wall. Find the angle between the ladder and the ground to the nearest degree.

In a right triangle, the side opposite angle $X$ measures $4\text{ cm}$ and the hypotenuse measures $7\text{ cm}$. Calculate angle $X$ in degrees to one decimal place.

In a right triangle, one acute angle $\theta$ satisfies $\sin \theta = \frac{4}{7}$ and the other acute angle is $\phi$. Calculate both $\theta$ and $\phi$ in degrees to the nearest whole number.

In a right triangle, the side adjacent to angle $\phi$ is 4 cm and the hypotenuse is 7 cm. Determine angle $\phi$ in degrees to the nearest tenth.