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

A right-angled sail has a vertical side of $8 \text{ m}$ and a horizontal base of $6 \text{ m}$. Find the angle $M$ at the base adjacent to the $6 \text{ m}$ side.

Find angle $G$ in a right triangle where the hypotenuse is 17 and the side adjacent to $G$ measures 15.

Find the angle $C$ in a right triangle where the hypotenuse is 10 and the side adjacent to $C$ is 6.

In a right triangle, the lengths of the legs are 5 and 12. Find the acute angle $D$ opposite the 5-unit side.

Calculate angle $E$ in a right triangle where the hypotenuse is 13 and the side adjacent to $E$ is 5.

A slide is 12 m long and reaches a horizontal run of 9 m. Determine the angle of descent $L$ relative to the horizontal.

In a right triangle, the hypotenuse measures 15 and the side opposite angle $B$ measures 9. Calculate the size of angle $B$.

A ramp rises $3\text{ m}$ over a horizontal distance of $20\text{ m}$. Find its incline angle $K$ above the horizontal.

In a right triangle, two legs measure $7 \text{ cm}$ and $24 \text{ cm}$. Find the acute angle $H$ opposite the $7 \text{ cm}$ side.

In a right triangle, the legs measure 8 and 15. Determine the angle $F$ opposite the 8-unit leg.

Find the angle $A$ in the right triangle shown below, given that the hypotenuse is 7 and the side opposite $A$ is 4. Give your answer correct to one decimal place.

A ladder $10 \text{ m}$ long leans against a wall so its base is $6 \text{ m}$ from the wall. Find the angle of elevation $\theta$ between the ladder and the ground.