Question

1. determine the area of the oblique triangle having the following measurements. round your answer to two decimal pla

b = 82°25, a = 10, and c = 15

a) 66.91 sq. units b) 89.21 sq. units c) 81.78 sq. units
d) 59.48 sq. units e) 74.34 sq. units

Explanation:

Step1: Convert angle to decimal degrees

First, convert \( 82^\circ 25' \) to decimal degrees. Since \( 1^\circ = 60' \), \( 25'=\frac{25}{60}\approx0.4167^\circ \), so \( B = 82 + 0.4167 = 82.4167^\circ \).

Step2: Use the area formula for oblique triangles

The formula for the area of an oblique triangle with two sides \( a, c \) and included angle \( B \) is \( \text{Area}=\frac{1}{2}ac\sin B \).
Substitute \( a = 10 \), \( c = 15 \), and \( B = 82.4167^\circ \) into the formula:
\( \text{Area}=\frac{1}{2}\times10\times15\times\sin(82.4167^\circ) \)
Calculate \( \sin(82.4167^\circ)\approx\sin(82.4167)\approx0.9914 \)
Then \( \text{Area}=\frac{1}{2}\times10\times15\times0.9914 = 75\times0.9914 = 74.355 \approx 74.34 \) (rounded to two decimal places).

Answer:

e) 74.34 sq. units