Q4 of 104 Page 193

In a rectangle ABCD, AB = 20, m∠BAC = 60, calculate the length of side and diagonals and.

∵ ∠BAC = 60

we know that

since, diagonals of any rectangle are always equal

⇒ AC = BD

Now

by Pythagoras theorem

AB² + BC² = AC²

⇒ 20² + BC² = 40²

⇒ BC = 20√3

Evaluate:

3cos²30 + sec²30 + 2cos0 + 3sin90 – tan²60

In ΔABC, m∠B = 90, find the measure of the parts of the triangle other than the ones which are given below:

(1) m∠C = 45, AB = 5

(2) m∠A = 30, AC = 10

(3) AC = 6√2, BC = 3√6

(4) AB = 4, BC = 4

If θ is measure of an acute angle and cosθ = sinθ, find the value of 2tan²θ + sin²θ + 1.

If α is measure of acute angle and 3sinα = 2cosα, prove that