Question

What is x? Round to nearest tenth.

Answer 1

67.4 degrees

Explanation:

We are given a right angled triangle,and with respect to x as theta,in which:

• Perpendicular = Let us find.
• Base = 5 units
• Hypotenuse = 13 units

To find:

Angle x as given in figure

To proceed,let us find the perpendicular.

Since the given figure is a right angled triangle, we can apply the pythagoras theorem,which says:

• a² + b² = c²

where a and b are legs of the triangle and c is the hypotenuse.

Putting the values,

• 5² + perpendicular² = 13²

On solving,

• 25 + p² = 169
• p² = 169-25 = 144 = 12²

On taking square root on both sides,

• p = 12 units

Hence perpendicular = 12 units

We know,tan∅ = Perpendicular/base

Putting the values,we get:

tan∅ = 12/5

Transposing tan to RHS:

∅ = 12/5*tan^-1

∅ = 67.4(To the nearest tenth)