Question

Special right triangles

Please help I don’t understand this at all step by step would be super appreciated

Answer 1

x=1.43

Explanation:

Remember the trigonometry concept.

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Which represents Sin∅ = p/h, Cos∅ = b/h, Tan∅= p/b.

The letters stand for:

h- hypotenuse which is the side opposite to the right angle.

b- base the side which has two angles.

p- perpendicular is the other side which is between the hypotenuse and base.

I will label everything in the triangle for you to understand.

Trigonometry involves finding the unknown side using a known angle and a known side or finding the unknown angle using two known sides.

We need at least one side from the triangle BCD. Both triangles share a common side CB so we can find that side and using that side we can find x.

The CB is perpendicular so we can use trigonometry to build an equation:

Sin 60°= CB/
`\sqrt[7]{3}`

`\sqrt[7]{3}` Sin 60°= CB

CB= 1.013189805= 1.01

If you see AD is a straight line so the total angle is 180° that means that angle ACB and BCD will equal 180°. That means that angle BCD is 180°-90°=90°

So we can also apply trigonometry to the triangle BCD.

Cos 45°= 1.01/x

x cos45°= 1.01

x= 1.01/cos45°

x= 1.428355698= 1.43

Remember that hypotenuse is the greatest side.