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# Trigonometry Question - Area of a Triangle watch

1. In the triangle XYZ, XY = 4.6 cm and YZ = 6.9 cm. The area of the triangle is 7.3cm^2. Find two possible values for ∠XYZ.

I've figured out one possible angle using the formula for the area of a triangle (27.4° ) but don't quite know how to get a second solution.

I'd be really grateful for some tips!

Thanks!
2. (Original post by grace15)
In the triangle XYZ, XY = 4.6 cm and YZ = 6.9 cm. The area of the triangle is 7.3cm^2. Find two possible values for ∠XYZ.

I've figured out one possible angle using the formula for the area of a triangle (27.4° ) but don't quite know how to get a second solution.

I'd be really grateful for some tips!

Thanks!
Without seeing your working, I presume you got to the stage where you had sin x = something, and then just found the inverse sine.

Note that sin x = sin (180 - x).

The sine graph is symmetrical about x= 90.

So if x is a solution to sin x = something, then 180-x is another solution.
3. Thank you so much!

(Original post by ghostwalker)
Without seeing your working, I presume you got to the stage where you had sin x = something, and then just found the inverse sine.

Note that sin x = sin (180 - x).

The sine graph is symmetrical about x= 90.

So if x is a solution to sin x = something, then 180-x is another solution.

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Updated: July 24, 2017
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