In Δ ABC, ∠B = 90º, AC = 29 cm and BC = 20 cm. Then \(\frac{{1 - \sin A + \cos A}}{{1 + \sin A + \cos A}}\) is equal to:
3/7
Given:
In the given triangle Δ ABC, ∠B = 90°, AC = 29 cm, BC = 20 cm.
Calculation:
As shown above, in triangle Δ ABC where AB, BC, and AC are given. Since (21, 20, 29) are Pythagorean triplets, AB is 21 cm.
Now, the values of sinA and cosA can be easily calculated from the figure above.
⇒ SinA = (Opposite)/(Hypotenuse) = BC/AC = 20/29
⇒ CosA = (Adjacent)/(Hypotenuse) = AB/AC = 21/29
Now, calculating (1 – sinA + cosA)/(1 + sinA + cosA) will yield the value
⇒ (1 – 20/29 + 21/29)/(1 + 20/29 + 21/29)
⇒ (1 + 1/29)/(1 + 41/29) = (30/29)/(70/29)
⇒ 30/70 = 3/7
∴ The value of (1 – sinA + cosA)/(1 + sinA + cosA) is 3/7.
Important Questions from Properties of Triangles
What is the perimeter of the triangle ?
Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of the statements given above is/are correct ?
What is the nature of the triangle ?
If c = 8, what is the area of the triangle ?
What is the value of n ?
