SOLUTION: Given triangle ABC, AB = 5cm and angle BAC is 40 degrees, use trigonometry to find the missing side BC. The triangle is right angled at B. (1dp) I know how to do trigonometry bu

Algebra ->  Triangles -> SOLUTION: Given triangle ABC, AB = 5cm and angle BAC is 40 degrees, use trigonometry to find the missing side BC. The triangle is right angled at B. (1dp) I know how to do trigonometry bu      Log On


   

Question 1027668: Given triangle ABC, AB = 5cm and angle BAC is 40 degrees, use trigonometry to find the missing side BC. The triangle is right angled at B. (1dp)
I know how to do trigonometry but for some reason I can't get this question. Thanks!
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
BA is the hypotenuse, but you do not need its value.
BC%2FAB=tan%2840%29

BC=AB%2Atan%2840%29
BC=5%2Atan%2840%29
BC=5%2A0.83910
BC=4.195

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you have a right triangle ABC, where angle B is the right angle.

you know that AB = 5 cm.

you know that angle BAC is 40 degrees.

you want to find the length of BC.

draw the triangle and you will see that BC is opposite angle BAC.

tan(40) is equal to opposite / adjacent.

opposite if BX
adjacent is AB.

if you let x equal the length of BC, then you get:

tan(40) = x/5

solve for x to get x = 5 * tan(40).

solve for x to get x = 4.195498156.

the length of BC is equal to 4.195498156.

this can be rounded as required, but i'll just leave it as what the calculator i used displayed it as.

the diagram i drew is shown below:

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