The height of a house is h and 5.2 m long ladder is just sufficient to go at the top of the house when its inclination with the horizontal ground is 45°. Find the height of the house.

Correct option is C

Given:

Length of the ladder = 5.2 m

Angle of inclination with the horizontal ground = 45°

Formula Used:

sin $$\theta =$$$$\frac{\text{Perpendicular}}{\text{Hypotenuse}}$$​​​

Solution:

Let , height of the house is h.

sin 45° = $$\frac{h}{5.2}$$ 

​​$$\frac1{\sqrt 2}$$ = $$\frac{h}{5.2}$$ 
h = $$\frac {5.2}{\sqrt 2}\times \frac {\sqrt 2}{\sqrt 2}$$ = $$\frac {52\sqrt 2}{2\times 10}$$ = $$\frac{13\sqrt 2}5$$ m​

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