geometry homework!!!!

Question

1) Assume that angle A is an acute triangle. If sin A= 0.994, use a calculator to find the measure of angle A to two decimal places.

2) When solving a right triangle , if you are given both acute angles is that sufficient information? Explain.

3) From a point 135 feet from the base of a tree, the angle from ground level to the top of the tree is 49 degrees. Find the height of the tree to the nearest foot.

Answer 1

1. sin A= 0.994

A = sin^-1(0.994)

A = 83.72°

Angle is less than 90° This is an acute angle.

2. A right triangle  is a triangle in which one angle is a right angle (that is, a 90 degree angle). 

the sum of the angles = 180°

angle1 + angle2 + angle 3 = 180°

angle1 + angle2 + 90 = 180°

angle1 + angle2  = 90°

sum of the angles are 90, so they are acute angles.

3. let h is the height of the tree
the height can be found using trigonometric relations

tan A = opposite side / adjacent height

tan 40 = h / 135

h = 135 * tan 40

h = 135 * 0.839

h = 113.278 ft.