Question

Unit 8: right triangles & trigonometry date: ________________________ per: _______ homework 2: special right triangles.

Answer 1

The sides and angles of a triangle can be determined using trigonometry ratios

The values of x, y and z are $x = 14\sqrt 2$, $y =14$ and $z = 14\sqrt 3$

How to determine the missing values of the triangle

The upper triangle is a right triangle with an angle measure of 45 degrees.

So, the value of x is:

$x = 14\sqrt 2$

Next, we calculate the hypotenuse (h) of the lower triangle using:

$h^2 = (14\sqrt 2)^2 + (14\sqrt 2)^2$

So, we have:

$h^2 = 784$

Take the square roots of both sides

$h = 28$

The value of y is then calculated using the following sine ratio

$\sin(30) = \frac y{28}$

Make y the subject

$y =28 * \sin(30)$

Evaluate

$y =14$

The value of z is then calculated using the following cosine ratio

$\cos(30) = \frac z{28}$

Make z the subject

$z =28 * \cos(30)$

Evaluate

$z =28 * \frac{\sqrt 3}{2}$

$z = 14\sqrt 3$

Hence, the values of x, y and z are $x = 14\sqrt 2$, $y =14$ and $z = 14\sqrt 3$

Read more about right triangles at:

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