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Chapter 8: Q. 10 (page 555)

Find the area of the triangle described in Problem 5.

Short Answer

Expert verified

The area of the triangle is $19.81$ square units.

Step by step solution

01

Step 1. Given Information

The given triangle is

02

Step 2. Find the Semiperimeter

The semiperimeter of the triangle is $\begin{array}{rcl} s & = & \frac{5 + 8 + 10}{2} \\ = & 11.5 \end{array}$

03

Step 3. Find the Area

The area of a triangle is given by the formula, $A = \sqrt{s (s - a) (s - b) (s - c)}$ .
Calculate the area.

$\begin{array}{rcl} A & = & \sqrt{11.5 \times 6.5 \times 3.5 \times 1.5} \\ = & \sqrt{392.4375} \\ \approx & 19.81 \end{array}$

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Most popular questions from this chapter

Write the formula for the distance $d$ from $P_{1} = (x_{1}, y_{1})$ to $P_{2} = (x_{2}, y_{2})$ .

Given two sides and the included angle, the first thing to do to solve the triangle is to use the Law of Sines .

Circumscribing a TriangleShow that $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} = \frac{1}{2 r}$

where $r$ is the radius of the circle circumscribing the triangle PQR whose sides are a, b, and c, as shown in the figure.

Area of a Segment Find the area of the segment of a circle whose radius is 5 inches, formed by a central angle of $40 °$ .

If $θ$ is an acute angle, solve the equation $\cos θ = \frac{\sqrt{2}}{2}$ .

See all solutions

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