Question

How do you solve the right triangle given`a=32m, A=46°`?

Answer 1

The angles are `90°, 46° and 44°`
The sides are `32m, 30.9m and 44.5m`

Explanation:

Let's call the triangle ABC, where `hatB` is the 90° angle.

The sum of the angles in a triangle is 180°

If `hatB = 90°,` then `hatA +hatC=90°`

From `hatA = 46°`, you can calculate `hatC`

`hatC = 90°-46° = 44°`

Using trigonometry to find the length of `AB or c`

`"opp"/"adj" = c/32 = tan44°`

`c = 32tan44°`3

`c = 30.9m`

The length of the hypotenuse, AC, can be found by using trig or Pythagoras's Theorem.

Pythagoras`color(white)(xxxxxxxxxxxxxxxxxx)` Trig

`a^2+ c^2 = b^2color(white)(xxxxxxxxcccccxxx xx)"a"/32 = 1/(cos44)`

`32^2 + 30.9^2 =1978.9color(white)(xxxxxxxxx)a = 32/(cos44)`

`sqrt1978.9 = 44.5mcolor(white)(xxxxxxxxxxx) a = 44.5m`