Question

a14. What are the lengths of b and c? Write your answer to the nearest tenth of a metre, where appropriate. b 5m 3 m-k3 m

Answer 1

As you can see in the diagram, there are two triangles. We will separate the two triangles into the smaller and the bigger one.

For the smaller triangle:

Now we will use the Pythagorean Theorem. The theorem states that the square of the longest side is equal to the sum of the squares of the two other sides.

To solve for the value of b, we will have:

`\begin{gathered} 5^2=3^2+b^2 \\ b^2=5^2-3^2 \\ b=\sqrt[]{5^2-3^2} \\ b=\sqrt[]{25-9} \\ b=\sqrt[]{16} \\ b=4 \end{gathered}`

For the bigger triangle:

We will also use the pythagorean theorem to find the value of c and by using the value of b we got from the smaller triangle.

`\begin{gathered} c^2=b^2+6^2 \\ c^2=4^2+6^2 \\ c=\sqrt[]{4^2+6^2} \\ c=\sqrt[]{16+36} \\ c=\sqrt[]{52} \\ c=2\sqrt[]{13} \\ c=7.211102551 \end{gathered}`

ANSWER:

b = 4 cm

c = 7.2 cm