In triangle $abc$, $m\angle a = 90^\circ$, $m\angle b = 75^\circ$, and $bc = \sqrt {3}$ units. what is the area of triangle $abc

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shutvik

2 months ago

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In triangle $abc$, $m\angle a = 90^\circ$, $m\angle b = 75^\circ$, and $bc = \sqrt {3}$ units. what is the area of triangle $abc

$? express your answer as a common fraction. your answer submittips give up

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-03-08T21:07:12+03:00

Given the specified angles, one is 90 degrees, indicating that the triangle is a right triangle. With provided angles and one side representing the hypotenuse (the longest side), the area is determined using the formula: Area = 1/2 * base * height. Let's compute the height and base:

From sin 75, we derive height = 1.67.
And from cos 75, we obtain base = 0.45.

Calculating area gives us Area = (0.45 * 1.67) / 2, resulting in 0.37 square units.

Thus, the triangle's area is approximately 0.37 square units.