Question

Please help me with this question

Answer 1

The missing sides of the right triangles are: Case A: x = 5.592 m, Case B: x = 9.949 m, Case C: x = 12.734 m, Case E: x = 1.847 m, Case F: x = 16.728 m, Case H: x = 46.175 m, Case I: x = 5.774 m, Case J: x = 3.654 m, Case K: x = 7.825 m

How to determine the missing sides of right triangles by trigonometric functions

In this question we find nine cases of missing sides in right triangles, every side can be found by means of trigonometric functions, which are defined below:

Sine:

`\sin \theta = (y)/(r)`

Cosine:

`\cos \theta = (x)/(r)`

Tangent:

`\tan \theta = (y)/(x)`

Where:

• x - Side adjacent to angle.
• y - Side opposite to angle.
• r - Hypotenuse

Now we proceed to determine all missing sides:

Case A:

x = (10 m) · sin 34º

x = 5.592 m

Case B:

x = (12 m) · sin 56º

x = 9.949 m

Case C:

x = (30 m) · tan 23º

x = 12.734 m

Case E:

x = (8 m) · tan 13º

x = 1.847 m

Case F:

x = (25 m) · cos 48º

x = 16.728 m

Case H:

x = (75 m) · cos 52º

x = 46.175 m

Case I:

x = (10 m) · tan 30º

x = 5.774 m

Case J:

x = (4 m) · sin 66º

x = 3.654 m

Case K:

x = (18 m) · cos 12º

x = 7.825 m