Hi there,
I have a problem involving a right angled triangle ABC. It is right angled at C.
The hypoteneuse has a value of 13 units.
A line stretches across the triangle from B to side AC at D. Side AC is divided into AD and DC. DC has the value 4 units.
Angle ABD equals x degrees and angle DBC equals 30 degrees.
I have to find the exact value of sin x.
I have worked out that side BC has a value of 6.928 units. Hypoteneuse BD has a value of 7.9 units and side AD equals 7 units.
Can anyone give me help with this problem please?
Thank you,
Cromlix
Too late...
I think the easiest thing is to use the law of sines for the triangle ABD. The angle ADB is . Therefore, .
A longer way is to say and rewrite as . Since , we have and so . This way we get a quadratic equation on .
The values you have calculated for BC and BD are approximately correct. But the question is asking for exact values. So instead of using a calculator, you should have used the fact that to get the exact value BC = , as in Archie Meade's comment. Also, BD is exactly 8 (not 7.9). But you are correct to say that AD = 7, and this is exact (because AC = 11 by Pythagoras, and when you subtract 4 for DC you are left with exactly 7 for AD). Now you can complete the question as in Archie's comment.