The floor of the entryway to an office building will be triangular. Two angles of the triangle will measure 40º, and the side between them will have a length of 8 meters. Make a scale drawing of the entryway using a scale 1 cm : 2 cm. Explain how you made your drawing.

The drawing in the attached figure

Step-by-step explanation:

we know that

An isosceles triangle, has two equal sides and two equal interior angles

In this problem, the floor of the entryway to an office building is in the shape of an isosceles triangle

step 1

Find the measure of the vertex angle

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

Let

x ---> the measure of the vertex angle of triangle

step 2

Find the length of the congruent sides of triangle

Applying the law of sines

Let

c ----> the length of one congruent side

we have

substitute

solve for b

step 2

Make a scale drawing of the entryway

The scale drawing is 1 cm : 2 cm

That means

1 cm in the drawing represent 2 cm in the actual

or

1 cm in the drawing represent 0.02 m in the actual

Find the dimensions in the drawing

For a=8 m

For b=5.22 m

step 3

Draw the triangle

see the attached figure

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)