Question

Solve the right angle (Picture provided)

Answer 1

The correct answer is option b

Explanation:

From the figure we can see that,a right angled triangle.

ΔABC

To find side AC

AC = √(AB)² - (BC)² =√15² - 12² = √81

AC = 9

To find the trigonometric ratio

Sin A = BC/AB = 12/15 = 4/5

Cos A = AC/AB = 9/15 = 3/5

Tan A = BC/AC = 4/3

Cosec A = 1/Sin A = 5/4

Sec A = 1/Cos A = 5/3

Cot A = 1/Tan A = 3/4

Therefore the correct answer is option b

Answer 2

B

Explanation:

Use the Pythagorean theorem for the right triangle ABC:

`AC^2+BC^2=AB^2,\\ \\AC^2=15^2-12^2,\\ \\AC^2=225-144,\\ \\AC^2=81,\\ \\AC=9\ cm.`

By the definition,

`\cos A=\frac{\text{adjacent leg}}{\text{hypotenuse}}=(AC)/(AB)=(9)/(15)=(3)/(5),\\ \\\sin A=\frac{\text{opposite leg}}{\text{hypotenuse}}=(BC)/(AB)=(12)/(15)=(4)/(5),\\ \\\sec A=(1)/(\cos A)=(1)/((3)/(5))=(5)/(3),\\ \\\csc A=(1)/(\sin A)=(1)/((4)/(5))=(5)/(4),\\ \\\tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}=(BC)/(AC)=(12)/(9)=(4)/(3),\\ \\\cot A=\frac{\text{adjacent leg}}{\text{opposite leg}}=(AC)/(BC)=(9)/(12)=(3)/(4).\\ \\`