Question

A right triangle has a hypotenuse of length 9 inches. If one angle is 35 degrees, find the length of each leg.

Answer 1

90 + 35 = 125.
180 -125 = 55 degrees.
 

4.59^2 + 6.55^2 = 8^2
21.1 + 42.9= 64 inches

Answer 2

Thus the perpendicular and base are 5.1622 and 7.3724.

Triangle

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Right angle triangle

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

A right triangle has a hypotenuse of a length of 9 inches.

And the angle is 35 degrees.

To find

The length of each side of the triangle.

How do find the length of each side of the triangle?

A right triangle has a hypotenuse of a length of 9 inches.

And the angle is 35 degrees.

Then the other sides are perpendicular and base.

According to sine rule. perpendicular will be,

$\begin{aligned} \rm sin \theta &= \rm \dfrac{perpendicular}{hypotenuse} \\\\\rm sin 35 &= \rm \dfrac{perpendicular}{9} \\\\0.5735 &= \rm \dfrac{perpendicular}{9}\\\\0.5735 * 9 &= \rm perpendicular\\\\\rm perpendicular &= 5.1622\\\end{aligned}$

Then according to the cosine rule. the base will be,

$\begin{aligned} \rm sin \theta &= \rm \dfrac{base}{hypotenuse} \\\\\rm sin 35 &= \rm \dfrac{base}{9} \\\\0.8191&= \rm \dfrac{base}{9}\\\\0.8191 * 9 &= \rm base\\\\\rm base&= 7.3724\\\end{aligned}$

Thus the perpendicular and base are 5.1622 and 7.3724.

More about the triangle link is given below.

https://brainly.com/question/25813512