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:
[tex]sin\theta = \frac{oppositeside}{hypotenuse} , cos\theta = \frac{adjacentside}{hypotenuse}, tan\theta= \frac{opposite side}{adjacent side}.[/tex]
To calculate, the angles we use
[tex]\theta = sin^{-1} (\frac{oppositeside}{hypotenuse}) , \theta = cos^{-1} (\frac{adjacentside}{hypotenuse}), \theta= tan^{-1} (\frac{opposite side}{adjacent side}).[/tex]
Step 2:
The triangle's angle = 85°, opposite side = a cm and adjacent side = 43 cm. So
[tex]tan\theta= \frac{opposite side}{adjacent side}.[/tex] [tex]tan85= \frac{a}{43}.[/tex], [tex]a = 11.430 (43) = 491.49 cm,[/tex]
Step 3:
The triangle's angle = 49°, opposite side = b m and adjacent side = 2.5 m. So
[tex]tan\theta= \frac{opposite side}{adjacent side}.[/tex] [tex]tan49= \frac{b}{2.5},[/tex] [tex]b = 1.150 (2.5) = 2.875 m.[/tex]
Step 4:
The triangle's angle = 44°, hypotenuse = c m and adjacent side = 94 m. So
[tex]cos\theta= \frac{adjacent side}{hypotenuse}.[/tex] [tex]cos44= \frac{94}{c},[/tex] [tex]c = \frac{94}{0.719} = 130.737 m.[/tex]
Step 5:
The triangle's angle = d°, opposite side = 1.8 m and hypotenuse = 35 cm = 3.55 m.
[tex]sin\theta= \frac{opposite side}{hypotenuse}.[/tex] [tex]sin d= \frac{1.8}{3.55},[/tex] [tex]d = sin^{-1} (\frac{1.8}{3.55}) = 30.464^{\circ}.[/tex]
Step 6:
The triangle's angle = e°, opposite side = 15.9 m and hypotenuse = 66 cm = 3.55 m.
[tex]sin\theta= \frac{opposite side}{hypotenuse}.[/tex] [tex]sin e= \frac{15.9}{66},[/tex] [tex]e = sin^{-1} (\frac{15.9}{66}) = 13.940^{\circ}.[/tex]
