Awoman stands at a horizontal distance \"x\" from a mountain and measures the angel of elevation of the mountaintop above the horizontal as \"θ.\" after walking a distance \"d\" closer to the mountain on ground level, she finds the angel to be \"φ.\" find a general equation for the height \"y\" of the mountain in terms of \"d\

A general equation for the height y of the mountain in terms of d is

First, let us recall the following formula about trigonometry.

Suppose the ΔABC is a right triangle at A, then:

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

The problem can be seen as shown in the picture in the attachment.

Look at ΔABC :

→ Equation 1

Look at ΔADC :

← Equation 1

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse

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