Question

Please help me and can you show full working

Answer 1

1. a = 491.49 cm,

2. b = 2.875 m,

3. c = 130.737 m,

4. d = 30.464°, and

5. e = 13.940 ° (sixth figure not visible).

Step-by-step explanation:

Step 1:

The three basic formula needed to solve these questions are:

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

To calculate, the angles we use

$\theta = sin^{-1} (\frac{oppositeside}{hypotenuse}) , \theta = cos^{-1} (\frac{adjacentside}{hypotenuse}), \theta= tan^{-1} (\frac{opposite side}{adjacent side}).$

Step 2:

The triangle's angle = 85°, opposite side = a cm and adjacent side = 43 cm. So

$tan\theta= \frac{opposite side}{adjacent side}.$ $tan85= \frac{a}{43}.$, $a = 11.430 (43) = 491.49 cm,$

Step 3:

The triangle's angle = 49°, opposite side = b m and adjacent side = 2.5 m. So

$tan\theta= \frac{opposite side}{adjacent side}.$ $tan49= \frac{b}{2.5},$ $b = 1.150 (2.5) = 2.875 m.$

Step 4:

The triangle's angle = 44°, hypotenuse = c m and adjacent side = 94 m. So

$cos\theta= \frac{adjacent side}{hypotenuse}.$ $cos44= \frac{94}{c},$ $c = \frac{94}{0.719} = 130.737 m.$

Step 5:

The triangle's angle = d°, opposite side = 1.8 m and hypotenuse = 35 cm = 3.55 m.

$sin\theta= \frac{opposite side}{hypotenuse}.$ $sin d= \frac{1.8}{3.55},$ $d = sin^{-1} (\frac{1.8}{3.55}) = 30.464^{\circ}.$

Step 6:

The triangle's angle = e°, opposite side = 15.9 m and hypotenuse = 66 cm = 3.55 m.

$sin\theta= \frac{opposite side}{hypotenuse}.$ $sin e= \frac{15.9}{66},$ $e = sin^{-1} (\frac{15.9}{66}) = 13.940^{\circ}.$