Unit 8 right triangles and trigonometry homework 1

The side x is an hypotenuse side to one of the right triangles formed by

altitude of the given triangle that has solid lines.

x is approximately 31.812

Reasons:

The figure shows a triangle with an altitude that forms two triangles inside

the main triangle.

By Pythagoras's theorem, we have;

For the right triangle on the left;

22² = h² + 16²

h² = 22² - 16² = 228

h² = 228

h = √228 = 2·√57

h = 2·√57

In the right triangle to the right, we have;

The length of the top base, b = 44 - 16 = 28

The square of the hypotenuse, x² = h² + b²

∴ x² = 228 + 28² = 1012

x = √(1012) = 2·√253

x = 2·√253 ≈ 31.812

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x = 31.8

Step-by-step explanation:

From the picture attached,

By applying Pythagoras theorem in right ΔADC,

AC² = AD² + CD²

(22)² = AD² + (16)²

AD² = 484 - 256

AD = √228

     = 2√57

Now we apply Pythagoras theorem in right ΔADB,

AB² = AD² + DB²

x² = 228 + (44 - 16)²

x² = 228 + 784

x² = 1012

x = √1012

  = 31.81

  ≈ 31.8