In △MDK, m=16.4, d=22, and k=19. Identify m∠D rounded to the nearest degree. The figure shows triangle M D K. The length of side

Question

2 years ago

11

M D is k units. The length of side D K is m units. The length of side K M is d units.
Answers;
a) 46°
b) 58°
c) 76°
d) 14°

1 answer:

Alex_Xolod [135] · Answer 1 · 2023-10-17T13:54:26+03:00

The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°

<h3>Which method can be used to find the measure of angle m<D?</h3>

In triangle ∆MDK, we have;

m = 16.4

d = 22

k = 19

Using cosine rule, we get;

d² = m² + k² - 2•m•k•cos(D)

Therefore;

2•m•k•cos(D) = m² + k² - d²

$D = arccos \left( \frac{ {m}^{2} + {k}^{2} - {d}^{2} }{2 \cdot m \cdot k} \right)$

Which gives;

$D = arccos \left( \frac{ {16.4}^{2} + {19}^{2} - {22}^{2} }{2 \times 16.4 \times 19} \right) \approx {76}^{ \circ}$

The correct option is therefore;

Learn more about the rule of cosines here:

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