Exercises: sin, cos and tan

According to industrial standards, the inclination angle of stairs should be $25 ° - 38 °$ for main stairs and $38 ° - 45 °$ for secondary stairs.

The storey height is 25m.

How long is the stair stringer for $25 °$ . Also calculate the projection.

For this task you need the following basic knowledge: Sine, Cosine and Tangent
Given: $h = 25 m$ ; $α = 25^{\circ}$
Required: $x$ , $w$
First calculate $x$ using the tangent.
$\tan (α) = \frac{h}{x}$
Solve for $x$ and plug in values.
$x = \frac{25 m}{\tan (25^{\circ})} \approx 54 m$
Compute $w$ using the sine.
$\sin (α) = \frac{h}{w}$
Solve for $w$ and plug in values.
$w = \frac{25 m}{\sin (25^{\circ})} \approx 59 m$
$\Rightarrow$ The projection is 54m and the stair length is 59m.
How long is the stair stringer for 38°. Also calculate the projection.

For this task you need the following basic knowledge: Sine, Cosine and Tangent
Given: $h = 25 m$ ; $α = 38^{\circ}$
Required: $x$ , $w$
First calculate $x$ using the tangent.
$\tan (α) = \frac{h}{x}$
Solve for $x$ and plug in values.
$x = \frac{25 m}{\tan (38^{\circ})} \approx 32 m$
Compute $w$ using the sine.
$\sin (α) = \frac{h}{w}$
Solve for $w$ and plug in values.
$w = \frac{25 m}{\sin (38^{\circ})} \approx 41 m$
$\Rightarrow$ The projection is $32 m$ and the stair length is $41 m$ .
How long is the stair stringer for 45°. Also calculate the projection.

For this task you need the following basic knowledge: Sine, Cosine and Tangent
Given: $h = 25 m$ ; $α = 45^{\circ}$
Required: $x$ , $w$
First calculate $x$ using the tangent.
$\tan (α) = \frac{h}{x}$
Solve for $x$ and plug in values.
$x = \frac{25 m}{\tan (45^{\circ})} = 25 m$
Compute $w$ using the sine.
$\sin (α) = \frac{h}{w}$
Solve for $w$ and plug in values.
$w = \frac{25 m}{\sin (45^{\circ})} \approx 35 m$
⇒ The projection is $25 m$ and the stair length is $35 m$ .

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