Chapter 7: Q27. (page 244)

Find the measure of each angle.
The measures of the acute angles of a right triangle are in the ratio $5 : 7$ .

Short Answer

Expert verified

The measures of each angle is $90^{\circ}, 37 \cdot 5^{\circ}$ and $52 \cdot 5^{\circ}$ .

Step by step solution

Step 1. Given information.

The ratio between acute angles of a right triangle is,

$5 : 7$

Step 2. Concept used.

The sum of angles of a triangle is $180^{\circ}$ .

And, one angle of a right triangle is $90^{\circ}$ $90^{\circ}$ .

Since, ratio of the angles is always in the simplified form,

It might not represent the actual measure.

Step 3. Considering the angles as5x and7x .

The sum of the angles of the triangle can be expressed using the above relation as,

$\begin{matrix} 5 x + 7 x = 90 \\ 12 x = 90 \\ x = 7.5 \end{matrix}$

So, each of the angles are given by,

$\begin{matrix} 5 x = 5 \times 7 \cdot 5 \\ 5 x = 37.5 \end{matrix}$

And,

$\begin{matrix} 7 x = 7 \times 7 \cdot 5 \\ 7 x = 52.5 \end{matrix}$

Therefore, the angles of right triangle are $90^{\circ}, 37 \cdot 5^{\circ}$ and $52 \cdot 5^{\circ}$ .

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Find the measure of each angle.
The measures of the acute angles of a right triangle are in the ratio $5 : 7$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Considering the angles as5x and7x .

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Find the measure of each angle.The measures of the acute angles of a right triangle are in the ratio5:7.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Considering the angles as5x and7x .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Logic and Functions

Mechanics Maths

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the measure of each angle.
The measures of the acute angles of a right triangle are in the ratio $5 : 7$ .