Question

From his house, Tristan could drive due north to get to his parents' house or he could drive due east to get to his grandparents' house. It is 6 miles from Tristan's house to his parents' house and a straight-line distance of 6.4 miles from his parents' house to his grandparents' house. How far is Tristan from his grandparents' house? If necessary, round to the nearest tenth.

Answer 1

`TG = 2.2`

Explanation:

Represent Tristan's house with T, his grandparent's with G and his parents with P.

Such that:

`TP = 6`

`GP = 6.4`

Required

Find TG

To solve this, we make use of Pythagoras Theorem which is represented as:

`GP^2 = TP^2 + TG^2`

Substitute values for GP and TP

`6.4^2 = 6^2 + TG^2`

`40.96 = 36 + TG^2`

Collect Like Terms

`TG^2 = 40.96 - 36`

`TG^2 = 4.96`

`TG = \sqrt{4.96`

`TG = 2.2` --- Approximated

Hence, the distance between Tristan ans his grandparent's house is 2.2 miles