Question

Construct a triangle with the given measures. Label all sides and angle measurements. 1. 4 cm, 6cm

Answer 1

Answer: angle = 33.7° ; angle =56.3 ° ;side AC = 7.2cm.

Given the two sides measurement,

• Assuming that the other side represent x and the other side represent y,( 4cm;6cm) , and that we are drawing a right angle triangle .We can constuct a triangle as follows :

• We can find the value of side h by using Pythagorean theorem:

`\begin{gathered} \text{ h = }\sqrt[]{x^2+y^2}\text{ } \\ \text{where x = 4}cm\text{ and y = 6}cm\text{ , } \\ \therefore\text{ h = }\sqrt[]{4^2+6^2} \\ \text{ = 7.2 }cm \end{gathered}`

• Subsequently, we will find angle angle , as shown in the diagram above as follows:

`\begin{gathered} \text{For angle }\beta \\ Tan\text{ }\beta\text{ = opposite /adjacent } \\ \text{Tan }\beta\text{ = }\frac{AB}{BC\text{ }} \\ Tan\text{ }\beta\text{ = }(6)/(4) \\ \beta\text{ = }\tan ^(-1)((6)/(4)) \\ \text{ =56.3}\degree \end{gathered}`

• Since we have angle ,= 56.3 °, ,we can find, angle :

,

• + + 90° = 180 °,....(angles in a triangle adds up to 180°)

∴ = 180° -90° -56.3°

=33.7°