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

Answer:

$TG = 2.2$

Step-by-step 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