|

Mathematics

Find the length of AB.

Trigonometric Identities

10 Likes

Answer

DE = CB = 30 cm

In Δ ADE,

$\text{tan 45°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ 1 = \dfrac{AE}{DE}\\[1em] ⇒ 1 = \dfrac{AE}{30}\\[1em] ⇒ AE = 30 cm$

In Δ DEB,

$\text{tan 60°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ \sqrt3 = \dfrac{EB}{DE}\\[1em] ⇒ \sqrt3 = \dfrac{EB}{30}\\[1em] ⇒ EB = 30\sqrt3 = 51.96$

AB = AE + EB

= 30 + 51.96 cm

= 81.96 cm

Hence, AB = 81.96 cm.

Answered By

7 Likes

Related Questions

Assertion (A): The length of the line AB is 100 m.
Reason (R): tan 45° = $\dfrac{50}{PB}$ ⇒ PB = 50 m and AB = 50 m + 50 m = 100 m
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
View Answer