Question

A right triangle has a hypotenuse of length 5.00 m, and one of its angles is 40.0°. What are the lengths of the following sides?(a) the side opposite the 40.0° angle_____ m(b) the side adjacent to the 40.0° angle_____ m

Answer 1

Given:

A right triangle has a hypotenuse of length 5.00 m, and one of its angles is 40.0°.

Required:

a) the side opposite the 40.0° angle.

(b) the side adjacent to the 40.0° angle.

Step-by-step explanation:

First draw a picture

Now, the trigonometric ratios

`cos\theta=(base)/(hypotenuse),sin\theta=(Perpendicular)/(Hypotenuse)`

So,

(a) The side opposite the 40.0° angle

`\begin{gathered} sin(40^(\circ))=(P)/(5) \\ P=5* sin(40^(\circ)) \\ P=3.2 \end{gathered}`

and

(b) The side adjacent to the 40.0° angle

`\begin{gathered} cos(40^(\circ))=(b)/(5) \\ b=5* cos(40^(\circ)) \\ b=3.8 \end{gathered}`

Answer:

The side opposite to 40 degree angle equal 3.2 m and side adjacent equal 3.8 m.