A fourth of the product of 13 and a number M
1 answer:
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Answer:
63.5
Step-by-step explanation:
The diagonals of a rhombus bisect opposite angles.
The longer diagonal bisects the 42° angle
The larger angle of the rhombus is 180 - 42 = 138
Let x = the length of the longer diagonal
You know two sides and the included angle of a triangle.
Using the law of cosines we get
x^2 = 34^2 + 34^2 - 2(34)(34) cos 138
= 1156 + 1156 - 2312 c0s 138
= 4030.1508...
x = sq rt 4030.1508...
= 63.5
The height of the tree is 60 meters.
Explanation:
Let the height of the tree be x. The tree casts a shadow of meters and the distance from the top of the tree to the end of the shadow is
meters.
The sides of the triangle are attached in the image below:
Using pythagoras theorem,
Expanding, we get,
Solving the equation using the quadratic formula , we get,
Simplifying, we have,
Thus,
and
where the value is not possible because substituting the value
in
results in negative solution. Which is not possible.
Hence, the value of x is 60.
Thus, The height of the tree is 60 meters.
