Jamal is 167 cm tall. which expression finds jamal's height in dekameters
2 answers:
Answer:
The height of Jamal's in dekameters is 0.167 dam.
Step-by-step explanation:
Given : Jamal is 167 cm tall.
To find : Which expression finds Jamal's height in dekameters ?
Solution :
To find the height in dekameters we will use the metric conversion,
Converting the unit centimeters to dekameters.
We know that,
1 centimeter = 0.001 dekameter.
i.e. 1 cm =0.001 dam.
So,
Therefore, the height of Jamal's in dekameters is 0.167 dam.
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See the picture attached to better understand the problem
we know that
in the right triangle ABC
cos A=AC/AB
cos A=1/3
so
1/3=AC/AB----->AB=3*AC-----> square----> AB²=9*AC²----> equation 1
applying the Pythagoras Theorem
BC²+AC²=AB²-----> 2²+AC²=AB²---> 4+AC²=AB²----> equation 2
substitute equation 1 in equation 2
4+AC²=9*AC²----> 8*AC²=4----> AC²=1/2----> AC=√2/2
so
AB²=9*AC²----> AB²=9*(√2/2)²----> AB=(3√2)/2
the answer is
the hypotenuse is (3√2)/2
we know that
in the right triangle ABC
cos A=AC/AB
cos A=1/3
so
1/3=AC/AB----->AB=3*AC-----> square----> AB²=9*AC²----> equation 1
applying the Pythagoras Theorem
BC²+AC²=AB²-----> 2²+AC²=AB²---> 4+AC²=AB²----> equation 2
substitute equation 1 in equation 2
4+AC²=9*AC²----> 8*AC²=4----> AC²=1/2----> AC=√2/2
so
AB²=9*AC²----> AB²=9*(√2/2)²----> AB=(3√2)/2
the answer is
the hypotenuse is (3√2)/2