Question

ABCD is a Trapezium, Work out the size of angle CDA to one decimal place

Answer 1

Answer:

32.3°

Step-by-step explanation:

Work out length of a (red) using Pythagoras:

b = 6, c = 7.5

a² + b² = c²

a² + 6² = 7.5²

a² + 36 = 56.25

a² = 56.25 - 36

a² = 20.25

a = √20.25 = 4.5cm

we now have a (in red on my diagram)

Working out the length in purple:

24 - 10 - 4.5 = 9.5cm

To find angle CDA in blue using Trig:

We have opposite side = 6 and adjacent side = 9.5

so we can use TOA

Tan θ = opposite / adjacent

Tan θ = 6 / 9.5

θ =tan⁻¹(6/9.5) = 32.3° (1dp)

Answer 2

Answer:

CDA≈27,6°

Step-by-step explanation:

First we solve the x using pythagorean theorem

a^2+b^2=c^2

x^2+6^2=6.5^2

x^2+36=42.25      ||-36

x^2=42.25-36

x^2=6.25               ||√

√x^2=√6.25

x=2.5cm

now we can solve y

y = 23cm-9cm-2.5cm

y=11.5cm

now we can solve CDA angle with tanα

tanα=$\frac{a}{b}$

tanα=6cm/11.5cm

α≈27,6°