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iren [92.7K]
3 years ago
15

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?
Mathematics
1 answer:
PtichkaEL [24]3 years ago
8 0

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

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