Question

For the right triangles below, find the exact values of the side lengths a and c. If necessary, write your responses in simplified radical form.

Answer 1

First triangle:
`a = 5√(2)`, second triangle:
`c = (8√(3))/(3)`

Explanation:

In the first triangle, the value of
`a` is equal to the following trigonometric relation:

`a = (5)/(\cos 45^(\circ))`

`a = (5)/((√(2))/(2) )`

`a = (10)/(√(2))`

`a = (10√(2))/(2)`

`a = 5√(2)`

In the second triangle, we obtain the value of
`c` is equal to the following trigonometric relation:

`c = 8\cdot \tan 30^(\circ)`

`c = 8 \cdot \left((\sin 30^(\circ))/(\cos 30^(\circ)) \right)`

`c = 8\cdot \left(((1)/(2) )/((√(3))/(2) ) \right)`

`c = (8)/(√(3))`

`c = (8√(3))/(3)`