Question

Find the height of the triangle 10 points!

Answer 1

Answer:

A. 3.4

Step-by-step explanation:

We have been given a graph of a right triangle and we are asked to find the height of our given right triangle.

Since we know that sine relates the opposite side of a right triangle to hypotenuse, so we will use sine to find height of our given triangle.

$\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{Sin}(20^{o})=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{Sin}(20^{o})=\frac{x}{10}$

$0.342020143326=\frac{x}{10}$

$0.342020143326\times 10=\frac{x}{10}\times 10$

$0.342020143326\times 10=x$

$x=03.42020143326\approx 3.4$

Therefore, the height of our given triangle is 3.4 units and option A is the correct choice.

Answer 2

By the 6 trigonometric ratios in a right triangle
 
(sine, cosine, tangent, cotangent, secant, cosecant)

we have the following:


$\displaystyle{ sin20^o= \frac{opposite \ side}{hypothenuse}= \frac{x}{10}$


So, $x=10\cdot sin20^o$


sin20° must be given, or can be found using a calculator:


Using the calculator of our pc: Calculator- view:Scientific- press 20 then sin button, we find : sin20°=0.342


$x=10\cdot sin20^o=10\cdot0.342=3.42$


Answer: A)3.4