Question

Solve for the variable shown

Y=

Answer 1

Answer:

y≈94.31

Step-by-step explanation:

Hi there!

We're given a right triangle (notice the 90 degree angle), the measure of one of the legs (one of the sides that make up the right angle) as 46, the other one as y, and one of the angles as 26°

We want to solve for y

We can use a trigonometric ratio to do that.

First, let's recall the three most-well known ratios:

Sine is $\frac{opposite}{hypotenuse}$

Cosine is $\frac{adjacent}{hypotenuse}$

Tangent is $\frac{opposite}{adjacent}$

Since we are given one of the angles, let's find out which sides are the opposite, adjacent, and hypotenuse, in reference to the given angle (the 26° angle)

In reference to that angle, the side opposite to that angle (also the side known as "opposite) is the side marked as 46, the adjacent side is y, and the hypotenuse is the unmarked side

Since we know the opposite and adjacent, let's use the ratio for tangent

Since we based our labels off of the 26 degree angle, the tangent ratio is the tangent OF 26, or tan(26)

tan(26)=$\frac{46}{y}$

Now we need to solve the equation

Start by multiplying both sides by y

tan(26)*y=46

Divide both sides by tan(26)

y=$\frac{46}{tan(26)}$

Plug $\frac{46}{tan(26)}$  into your calculator, and remember to have the calculator on degree mode

$\frac{46}{tan(26)}$≈94.31

Remember that $\frac{46}{tan(26)}$ is equal to y, which means that y is about 94.31

Hope this helps!