IB Mathematics Applications & Interpretation Question Type 1: Using SOH CAH TOA to Find One Side Length Given an Angle Exercises

In a right-angled triangle, the side opposite to angle $\theta$ has a length of $6$ and the side adjacent to angle $\theta$ has a length of $8$.

Determine the size of angle $\theta$.

In a right triangle, the side adjacent to angle $\theta =60^{\circ }$ is $4$. Find the length of the opposite side.

In a right triangle, the opposite side is $9$ and the adjacent side is $12$. Find angle $\theta$.

In a right triangle, the hypotenuse is $15$ and the adjacent side to angle $\theta$ is $12$. Find $\theta$.

In a right-angled triangle, the hypotenuse measures $10$ and an angle $\theta =30^{\circ }$. Find the length of the side adjacent to the angle $\theta$.

In a right-angled triangle, the side opposite to angle $\theta =25^{\circ }$ has a length of $3$. Determine the length of the hypotenuse.

In a right triangle, the hypotenuse is $5$ and angle $\theta =45^{\circ }$. Find the length of the opposite side.

In a right triangle, the adjacent side to angle $\theta =20^{\circ }$ is $8\text{ cm}$. Find the length of the hypotenuse.

In a right triangle, the hypotenuse is $10$ and angle $\theta =30^{\circ }$. Find the length of the opposite side.

In a right-angled triangle, the side adjacent to angle $\theta =60^{\circ }$ has a length of $4$. Calculate the length of the hypotenuse.

In a right triangle, the hypotenuse is $5$ and angle $\theta =45^{\circ }$. Find the length of the adjacent side.

In a right triangle, the hypotenuse is $7$ and the side opposite to angle $\theta$ is $4$. Calculate the value of $\theta$, giving your answer correct to two decimal places.