Question

Solve the right triangle. If two sides are given, give angles in degrees and minutes.

A = 12° 33', c = 283 ft
Round side lengths to two decimal places.

Answer 1

We are given angle A = 12° 33' and side c = 283 ft. Let's first find angle C using the sine ratio:

sin C = opposite / hypotenuse
sin C = a / c
a = c * sin C

Using a calculator:

sin C = sin(90° - A) ≈ 0.996
a ≈ 282.95 ft

Therefore, we have side a ≈ 282.95 ft. To find the remaining side b, we can use the Pythagorean theorem:

b² = c² - a²
b² = (283 ft)² - (282.95 ft)²
b ≈ 0.79 ft

(Note that we may have some rounding error in the last digit due to using approximate values for a and c, but it should be insignificant.)

Now let's find the angles:

Angle B = 90° - A ≈ 77° 27'

Using the sine ratio again:

sin B = opposite / hypotenuse
sin B = b / c
B ≈ 1.03°

(Note that we may have some rounding error here due to using an approximate value for b, but it should be insignificant compared to the precision of the given angles.)

Therefore, the angles of the right triangle are approximately:

A = 12° 33'
B ≈ 1.03°
C ≈ 76° 27'