Question

In right angled ∆ABC, ZA= 90°, AB= 8 cm., BC = 17 cm.
Find Sin B, Cos B. Also prove that tan B x tan (90 - B)=1.​​

Answer 1

Answer:

SinB = 15/17

CosB = 8/17

Step-by-step explanation:

Since Triangle is right angle triangle.

So, By using Pythagoras theorem we can find the length of remaining side (in this case base).

AB= 8cm, BC = 17 cm

AC = √{(BC)^2 - (AB)^2} = √{17^2 - 8^2} = 15

SinB = AC/BC = 15/17

CosB = AB/BC = 8/17

tanB = AC/AB = 15/8

Since Angle ( A+B+C) = 180

Angle (90+B+C) = 180

Angle (B+C) = 90

so, Angle (C) = 90- Angle (B)

Now, tan(90- B) = tanC = 8/15

tanB × tan (90-B) = 15/8 × 8/15 = 1