Question

8. An Isosceles triangle HIJ has sides HI and HJ as 19 meters each. If angle I and angle J are 67 degrees, what is the distance of IJ?

Answer 1

Answer:

$IJ=14.8$

Step-by-step explanation:

In a triangle the sum of all angle measures is always 180 degrees

$A+B+C=180$

$2(67)+C=180$

$C=46$ degrees

By splitting the isosceles triangle down the middle we can calculate the base

So ∠H = 23°, ∠K = 90°, ∠J = 67°, HJ = 19

With this we can solve for half of the base. the trig function will need to use is sin, since the side opposite of ∠H will be part of the base. $sin=\frac{opposite}{hypotenuse}$

now we need to rearrange the formula for what we have.

$hypotenuse(sin)=opposite$

$19sin(23)=7.423$

This value is only half of the base, so we need to double it

$IJ=2(7.423)=14.8$