Question

From a window, h metres high above the ground, of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are α and β respectively. Show that the height of the opposite house is h(1+tanα.cotβ) metres

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The height of the opposite house is h(1+tanα.cotβ) metres

Step-by-step explanation:

Step 1:

Let B be the window of a house AB and let CD be the other house. Then, AB= EC =h metres.

Let CD = H metres. Then, ED= (H-h) m

Step 2:

In ∆BED,

cotα = BE/ED

BE = (H-h) cotα ... (a)

In ∆ACB,

Step 3:

AC/AB = cotβ

AC=h.cotβ …. (b)

But BE=AC

Step 4:

(H-h) cotα = hcotβ

$\mathrm{H}=\mathrm{h} \frac{(\cot \alpha+\cot \beta)}{\cot \alpha}$

Step 5:

H = h(1+tanα cotβ)