# How do you find the height of a triangle with the hypotenuse and base?

## How do you find the height of a triangle with the hypotenuse and base?

If only the base and hypotenuse of a right triangle are given, then before finding the area of the triangle, we first need to find the height using the Pythagoras theorem. Then we can use the formula 1/2 × base x height to find its area. height = √[(hypotenuse)2 – (base)2] = √(52 – 42) = √9 = 3 cm.

### Is hypotenuse the height of a triangle?

The base and height of a right triangle are always the sides adjacent to the right angle, and the hypotenuse is the longest side.

#### How do I find the height of a triangle?

How to Calculate the Height of a Triangle. Triangle height, also referred to as its altitude, can be solved using a simple formula using the length of the base and the area. Thus, the height or altitude of a triangle h is equal to 2 times the area T divided by the length of base b.

What is the easiest way to find the height of a triangle?

How to find the height of a triangle – formulas

1. area = b * h / 2 , where b is a base, h – height.
2. so h = 2 * area / b.

How to find the height of a right triangle?

The Pythagorean Theorem solution works on right triangles, isosceles triangles, and equilateral triangles. It will not work on scalene triangles! Using the area formula to find height The formula for the area of a triangle is 1 2 base × height 1 2 b a s e × h e i g h t, or 1 2 bh 1 2 b h.

## How to calculate the hypotenuse of a right triangle?

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²) Given angle and one leg. c = a / sin(α) = b / sin(β), from the law of sines. Given area and one leg.

### Where is the base and height of a triangle?

In this example, the shorter lengths of the triangle (the base and height) are on the left side of the equation whereas the longest side (the hypotenuse) is on the right side. Let’s use the pythagorean theorem to solve for the base of the triangle below:

#### What’s the formula for the area of a triangle?

The Pythagorean Theorem solution works on right triangles, isosceles triangles, and equilateral triangles. It will not work on scalene triangles! The formula for the area of a triangle is 1 2 base × height 1 2 b a s e × h e i g h t, or 1 2 bh 1 2 b h.