W explainations Right Triangle Trigonometry Quiz

• 5 units

• 10 units

• 8.66 units

• 7 units

Answer explanation

In a right triangle with a 30° angle, the side opposite this angle is half the length of the hypotenuse. Here, the hypotenuse is 10 units, so the opposite side is 10/2 = 5 units. Thus, the correct answer is 5 units.

• 7 units

• 10 units

• 9.9 units

• 7\sqrt{2} units

Answer explanation

In a right triangle with a 45° angle, the sides are in a 1:1 ratio. If the adjacent side is 7 units, the opposite side is also 7 units. Using the Pythagorean theorem, hypotenuse = √(7² + 7²) = 7√2 units.

• 10 units

• 5.78

• 8 units

• 6 units

Answer explanation

In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse. Here, sin(60°) = opposite/hypotenuse = 5/hypotenuse. Thus, hypotenuse = 5/sin(60°) = 5.78 rounded

In a right triangle, the hypotenuse is 13 units and one of the legs is 5 units. Find the length of the other leg.

• 12 units

• 10 units

• 8 units

• 9 units

Answer explanation

Using the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. Here, 5² + b² = 13². This simplifies to 25 + b² = 169. Thus, b² = 144, and b = 12. Therefore, the length of the other leg is 12 units.

Answer explanation

To find angle \(\theta\), use \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{4}{3}\). Thus, \(\theta = \tan^{-1}(\frac{4}{3}) \approx 53.13^\circ\). Therefore, the correct answer is \(53.13^\circ\).

Answer explanation

To find angle \( \theta \), use the sine function: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{10} = 0.8 \). Thus, \( \theta = \sin^{-1}(0.8) \approx 53.13^\circ \). The correct answer is \( 53.13^\circ \).

• 7 units

• 10 units

• 14\sqrt{2} units

• 7\sqrt{2} units

Answer explanation

In a 45-45-90 triangle, the legs are equal and each leg is \( \frac{hypotenuse}{\sqrt{2}} \). Thus, each leg is \( \frac{14}{\sqrt{2}} = 7\sqrt{2} \) units. 9.9 approx

Answer explanation

To find angle \(\theta\), use the cosine function: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9}{15} = 0.6\). Thus, inverse cosine (9/15) = 53.13 degrees approx.

• 8 units

• 13.86 units

• 14 units

• 12 units

Answer explanation

In a right triangle, the length of the side adjacent to a 30° angle can be found using the cosine function: adjacent = hypotenuse * cos(30°). Thus, adjacent = 16 * (√3/2) ≈ 13.86 units.

Answer explanation

To find angle use Inverse tangent (6/8). aprrox. 36.87