Question

question in △pqr, r = 4 inches, p = 8.4 inches and ∠q = 174°. find the area of △pqr, to the nearest 10th of a square inch. answer attempt 1 out of 2 in² submit answer watch video show examples

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle given two - sides and the included angle is $A=\frac{1}{2}rp\sin Q$.

Step2: Substitute the given values

We are given that $r = 4$ inches, $p=8.4$ inches, and $Q = 174^{\circ}$. Substitute these values into the formula: $A=\frac{1}{2}(4)(8.4)\sin(174^{\circ})$.

Step3: Calculate the sine value

First, find $\sin(174^{\circ})\approx0.1045$.

Step4: Calculate the area

Then, $A=\frac{1}{2}(4)(8.4)(0.1045)$.
$A = 2\times8.4\times0.1045$.
$A=16.8\times0.1045$.
$A\approx1.8$ square inches.

Answer:

$1.8$ square inches