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Gabriel leans a 18-foot ladder against a wall so that it forms an angle of 73^{\circ} ∘ with the ground. how high up the wall does the ladder reach? round your answer to the nearest hundredth of a foot if necessary.

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oladayoademosu

How high up the wall does the ladder reach is 17.21 ft.

To solve the question, we need to know what right-angled triangles are.

What is a right-angled triangle?

A right-angled triangle is a triangle in which the angle facing the longest side is 90°.

The required right-angled triangle

The ladder, the ground and the wall form a right angled triangle with hyptenuse side, length of ladder, L and opposite side to angle between ground and ladder, Ф = 73° is h. Opposite side equals height of ladder along wall, h.

How high up the wall does the ladder reach?

From trigonometric ratios

sinФ = h/L

h = LsinФ

Substituting the values of the variables into the equation, we have

h = LsinФ

h = 18 ft × sin73°

h = 18 ft × 0.9563

h = 17.21 ft

So, how high up the wall does the ladder reach is 17.21 ft.

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