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Chapter 5: Problem 18

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$A=60^{\circ}, \quad a=9, \quad c=10$$

Short Answer

Expert verified
The measurements of the triangle are approximately: Angle C = [value calculated in step 1], Angle B = [value calculated in step 2], and the length of Side b = [value calculated in step 3]. All these values should be rounded to two decimal places.

Step by step solution

01

Find Angle C

First, find the angle C by using the Law of Sines. The law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. Here we know that side a is opposite to angle A and side c is opposite to angle C. So the ratio a/sinA=c/sinC. Thus, \sin C = \frac{c \cdot \sin A}{a} = \frac{10 \cdot \sin 60掳}{9}
02

Calculate Angle B

Angle B can be calculated as the difference between 180掳 and the sum of angles A and C, as in any triangle, the sum of all angles is always 180掳. So, B = 180掳 - A - C.
03

Find Side b

The length of side b can be calculated using the Law of Sines. b/sinB=a/sinA. Thus, \( b = \frac{a \cdot \sin B}{\sin A} = \frac{9 \cdot \sin (180掳 - 60掳 - C)}{\sin 60掳} \)

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