Question

What is the length of one leg of the triangle?

Answer 1

Answer:

$5\sqrt{10}\ units$

Step-by-step explanation:

Let

x------> the length of one leg of the triangle

we know that

In the right triangle of the figure

$cos(45\°)=\frac{x}{10\sqrt{5}}$

and remember that

$cos(45\°)=\frac{\sqrt{2}}{2}$

so

$\frac{\sqrt{2}}{2}=\frac{x}{10\sqrt{5}}$

$x=(\sqrt{2}*10\sqrt{5})/2$

$x=5\sqrt{10}\ units$

Answer 2

The length of one leg of the triangle $\boxed{5\sqrt {10} }.$

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

Isosceles triangle has 2 sides equal to each other and the two base angles are equal to each other.

Given:

The length of the hypotenuse is $10\sqrt 5.$

The options are as follows,

(A). $5\sqrt 5$

(B). $5\sqrt {10}$

(C). $10\sqrt {5}$

(D). $10\sqrt {10}$

Explanation:

The length of the hypotenuse is $10\sqrt 5.$

Consider the length of other leg of the triangle $x$.

Use the Pythagoras formula in triangle ABC.

$\begin{aligned}{\left( {10\sqrt 5 }\right)^2}&= {\left( x \right)^2} + {\left( x \right)^2}\\100 \times 5&= 2{x^2}\\\frac{{500}}{2}&= {x^2}\\250&= {x^2}\\\end{aligned}$

Further solve the above equation.

$\begin{aligned}{x^2}&= 250\\x&= \sqrt {250}\\x&= 5\sqrt {10} \\\end{aligned}$

Hence, the length of one leg of the triangle $\boxed{5\sqrt {10} }.$

Option (A) is not correct.

Option (B) is correct.

Option (C) is not correct.

Option (D) is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: length of the leg, triangle, isosceles,perpendicular bisectors, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions, Pythagoras theorem, formula.