Right Triangle Trigonometry Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

In a right triangle with angle

\theta = 45°

and hypotenuse

= 8

, find both legs.

1
Step 1: Use $\sin 45° = \frac{\text{opp}}{8}$ . Since $\sin 45° = \frac{\sqrt{2}}{2}$ , the opposite leg $= 8 \cdot \frac{\sqrt{2}}{2} = 4\sqrt{2}$ .
2
Step 2: By symmetry (45-45-90 triangle), both legs are equal, so the adjacent leg also $= 4\sqrt{2} \approx 5.66$ .

Answer

Both legs

= 4\sqrt{2} \approx 5.66

In a 45-45-90 right triangle, both acute angles are equal (45°), so the two legs must be equal. Using

\sin 45° = \frac{\sqrt{2}}{2}

and the given hypotenuse gives each leg as

\frac{\sqrt{2}}{2} \times 8 = 4\sqrt{2}

About Right Triangle Trigonometry

The three primary trigonometric ratios—sine, cosine, and tangent—defined as ratios of specific sides in a right triangle.

In a right triangle, the angle [formula], and the hypotenuse is 10. Find the lengths of the opposite

A ladder 13 feet long leans against a wall. The base of the ladder is 5 feet from the wall. Find the

From the top of a 50-meter tall lighthouse, the angle of depression to a boat is [formula]. How far