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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.

Sagot :

MrRoyal

Answer:

[tex]TG = 2.2[/tex]

Step-by-step explanation:

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

Such that:

[tex]TP = 6[/tex]

[tex]GP = 6.4[/tex]

Required

Find TG

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

[tex]GP^2 = TP^2 + TG^2[/tex]

Substitute values for GP and TP

[tex]6.4^2 = 6^2 + TG^2[/tex]

[tex]40.96 = 36 + TG^2[/tex]

Collect Like Terms

[tex]TG^2 = 40.96 - 36[/tex]

[tex]TG^2 = 4.96[/tex]

[tex]TG = \sqrt{4.96[/tex]

[tex]TG = 2.2[/tex] --- Approximated

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

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