Question

3)
a right triangle with one leg length 15, one acute angle 87°, find the length of the other leg marked as $x$
(35.3)
tan
ten=
4)
a right triangle with one leg length 10, one acute angle 31°, find the length of the hypotenuse marked as $x$

Explanation:

Step1: Solve first triangle for $x$

Identify adjacent side to $87^\circ$ is $x$, opposite side is $15$. Use tangent:
$\tan(87^\circ) = \frac{15}{x}$
Rearrange to solve for $x$:
$x = \frac{15}{\tan(87^\circ)}$
Calculate $\tan(87^\circ) \approx 19.0811$, so:
$x \approx \frac{15}{19.0811} \approx 0.786$

Step2: Solve second triangle for $x$

Identify adjacent side to $31^\circ$ is $10$, hypotenuse is $x$. Use cosine:
$\cos(31^\circ) = \frac{10}{x}$
Rearrange to solve for $x$:
$x = \frac{10}{\cos(31^\circ)}$
Calculate $\cos(31^\circ) \approx 0.8572$, so:
$x \approx \frac{10}{0.8572} \approx 11.67$

Answer:

1. For the first triangle: $x \approx 0.79$
2. For the second triangle: $x \approx 11.67$