Question

Help with trig homework please

Answer 1

x = 38.5330 degrees

Explanation:

Remark

This is a sine law problem. I would check to see if it is going to work. Draw a perpendicular from the unmarked third angle to the base of the triangle. You are finding the height of the triangle. 2.8 must be greater than this height or the triangle has no solution.

Sin(20) = h/5.1 Multiply both sides by 5.1

5.1 * sin(20) = h

5.1 * 0.3420 = h

h = 1.744

Conclusion

Since 2.8 > 1.744 we do have a triangle [It was possible that we did not]7

Equation

Sin(x) / 5.1 = sin(20) / 2.8 Multiply both sides by 5.1

Solution

• sin(x) = 5.1 * sin(20) / 2.8 Do the division
• sin(x) = (5.1/2.8) * sin(20)
• sin(x) = 1.8214 * sin(20) Multiply by sin(20)
• sin(x) = 0.62297 Take the inverse sine of 0.62297
• x = sin-1(0.62297)
• x = 38.5330 degrees Answer

Answer 2

x = 38.5 degrees

Explanation:

We can solve this problem using the law of sins

sin A sin B

------------- = ----------------

a b

sin x sin 20

------------- = ----------------

5.1 2.8

Using cross products

2.8 sin x = 5.1 sin 20

Divide by 2.8 on each side

sin x = 5.1/2.8 sin 20

Take the arcsin of each side

arcsin sin x = arcsin (5.1/2.8 sin 20)

x = arcsin (5.1/2.8 sin 20)

x = 38.53299837

To one decimal place

x = 38.5 degrees