Chapter 9.7, Problem 10PSA

a

To determine

To find: The ratio of the longer leg to the hypotenuse in a $30°-60°-90°$ triangle

Answer to Problem 10PSA

The required ratio $2:\sqrt{3}$

Explanation of Solution

Given information :

Right triangle $30°-60°-90°$

Formula used :

Trigonometric formula

Calculation :

In triangle ABC, AC is hypotenuse, AC is perpendicular and BC is base for reference angle C

  

  $\frac{\text{AC}}{\text{BC}}=\sec 30=\frac{2}{\sqrt{3}}$

Hence, required ratio is $2:\sqrt{3}$

b

To determine

To find: The ratio of the longer leg to the hypotenuse in a $45°-45°-90°$ triangle

Answer to Problem 10PSA

The required ratio $1:\sqrt{2}$

Explanation of Solution

Given information :

Right triangle $45°-45°-90°$

Formula used :

Trigonometric formula

Calculation :

In triangle ABC, AC is hypotenuse, AC is perpendicular and BC is base for reference angle C

  

  $\frac{\text{AC}}{\text{BC}}=\sec 45=\frac{\sqrt{2}}{1}$

Hence, required ratio is $\sqrt{2}:1$