Mathematics: Solve the triangle. Triangle A B C has a vertex angle labeled C that measures 64 degrees, a base angle labeled B that measures 53 degrees, and a base angle labeled A that does not have a given measurement. The side connecting angle A to angle C is labeled b. The side connecting angle C to angle B is labeled a and measures 10 units. The base leg connecting angle B to angle A is labeled c. 64 degrees a equals 10 53 degrees b c Upper C A

oofStep-by-step explanation:...

Solve the triangle. Triangle A B C has a vertex angle

cassiegagnier73

21.01.2022

A=73°, b=8.35 Units, c=9.4 Units

Step-by-step explanation:

To solve a triangle completely means to find all its sides and angles.

First, we determine Angle A.

53°+64°+A=180° (Sum of Angles in a Triangle)

107°+ A=180°

A=180°-107° =73°

Next, we determine the lengths of AC and AB.

Using Sine Rule

$\frac{a}{Sin A}= \frac{b}{Sin B}$

$\frac{10}{Sin 73}= \frac{b}{Sin 53 }$

Criss multiplying

b X sin73 = 10 X Sin 53

$b= \frac{10 X Sin 53}{Sin 73 }$

b=8.35 Units

Similarly, for c

$\frac{a}{Sin A}= \frac{c}{Sin C}$

$\frac{10}{Sin 73}= \frac{c}{Sin 64 }$

Criss multiplying

c X sin73 = 10 X Sin 64

$b= \frac{10 X Sin 64}{Sin 73 }$

c=9.4 Units

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