In the triangle below, determine the value of a.

Mathematics

1 answer:

makkiz [27]2 years ago

4 0

Answer:

Step-by-step explanation:

This is classic right triangle trig. Side a, our unknown, is adjacent to angle C which is a given. You always have to use a given angle and side to find a missing side, so we have to figure out how the two givens are related to our unknown. Side a is adjacent to angle C, and we are also given the hypotenuse. We know side a is not the hypotenuse since the hypotenuse is ALWAYS the side across from the 90 degree angle. The tan ratio of angle C will give us a way to have only one unknown.

tan 43 = a/26 and

26 tan 43 = a

Use your calculator now to find the missing side.

a = 24.2 units long

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F(x) = 4x^2 - 3x + 2kx + 1

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$\sqrt{\Delta_k}=\sqrt{256}=16\\\\k_1=\frac{12-16}{2\cdot4}=\frac{-4}{8}=-\frac{1}{2};\ k_2=\frac{12+16}{2\cdot4}=\frac{28}{8}=\frac{7}{2}\\\\a_k=4 > 0\ (up\ parabola\ arms-see\ the\ picture)\\\\Answer:k\in(-\infty;-\frac{1}{2})\ \cup\ (\frac{7}{2};\ \infty)$