Question

Which statements about the right triangle are correct

Answer 1

The statements 2, 4, and 5 are correct about the right-angled triangle.

Step-by-step explanation:

Step 1:

The formulae needed to solve the problem are;

$sin\theta = \frac{oppositeside}{hypotenuse} , cos\theta = \frac{adjacent side}{hypotenuse}, tan\theta = \frac{opposite side}{adjacentside},$

$cosec\theta = \frac{hypotenuse}{oppositeside} , sec\theta = \frac{hypotenuse}{adjacent side}, cot\theta = \frac{adjacent side}{oppositeside}.$

Step 2:

If the angle is B, the opposite side measures 5 units, the adjacent side measures 12 units, and the hypotenuse measures 13 units.

$cos B = \frac{12}{13} , sec B = \frac{13}{12} .$

Step 3:

If the angle is A, the opposite side measures 12 units, the adjacent side measures 5 units, and the hypotenuse measures 13 units.

$cot A = \frac{5}{12} , cosecA = \frac{13}{12} , sinA =\frac{12}{13} , tan A = \frac{12}{5}$.

Of the six given options, options $cot A = \frac{5}{12}, sinA =\frac{12}{13} ,sec B = \frac{13}{12}$ are the right options.