Solve the triangle below without using either the cosine or tangent ratios

Question

1. Solve the triangle below without using either the cosine or tangent ratios. Show your work. (15 points)

1. 

2. A fireman is heading towards a forest fire and needs to know how far away the fire is. The person in the fire tower can determine the distances and the angle shown below. What is the distance from the fireman to the fire? Show your work. (15 points)

1. 

Answer 1

The question doesn't say you can't use the sine function, so sin23^o = a/16 or a = 16 x 0.391 = 6.3.

b can be obtained from the pythagorean theorem b² = 16² - 6.3² = 216, b = 14.7

Connecting the fire hat with fire results in a right triangle whose hypotenuse is the distance from the fire hat to the fire. Use the pythagorean theorem again. D² = 2.1² + 3.2² , D = 3.8 miles

Answer 2

1.

To solve for the triangle, you can use trig, in this case sin.

Sin = opposite / hypotenuse

Sin(23) = a/16

To find b, we can still use sin but need to find the opposing angle.

The interior angles inside of a triangle must add up to 180. 23 + 90 + B = 180.

Angle B is thus 67 degrees.

Sin(67) = b/16

2.

Because the angle is 90 degrees, we have a right triangle. Thus, we can use the Pythagorean theorem to solve for the distance between the fire and the fireman

c²=a²+b²