Question

Consider a right triangle with leg b = 7.1 and opposite angle B = 39.3. Using a calculator, determine the other angle and the remaining sides of the triangle. Express your answers using at least one decimal place.

Answer 1

i. a = 8.7, b = 7.1 and c = 11.2

ii. A =
`50.7^(o)`, B =
`39.3^(o)` and C =
`90^(o)`

Explanation:

Given a right triangle with, b = 7.1 and B =
`39.3^(o)`.

I. Applying the trigonometric function to determine leg a, we have;

Tan θ =
`(opposite)/(adjacent)`

Tan
`39.3^(o)` =
`(7.1)/(a)`

a =
`(7.1)/(Tan 39.3^(o) )`

= 8.675

The length of leg a is 8.7.

ii. To determine leg c,

Sin
`39.3^(o)` =
`(opposite)/(hypotenuse)`

=
`(7.1)/(c)`

⇒c =
`(7.1)/(Sin39.3^(o) )`

= 11.21

The length of leg c is 11.2.

iii. Given that: B =
`39.3^(o)` and C =
`90^(o)`

Then,

A + B + C =
`180^(o)` (sum of angles at a point)

A +
`39.3^(o)` +
`90^(o)` =
`180^(o)`

A +
`129.3^(o)` =
`180^(o)`

A =
`180^(o)` -
`129.3^(o)`

=
`50.7^(o)`