The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? 5 StartRoot 2 EndRoot units 4 StartRoot 3 EndRoot units 10 StartRoot 2 EndRoot units 16 StartRoot 5 EndRoot units

The altitude is 4√3 units long

Step-by-step explanation:

Since the triangle is equilateral, all the sides will measure 8 units.

Now to find the altitude, we drop a line from the middle vertex to the horizontal line below and this splits the horizontal line into 2 equal parts which measures 4 units exactly.

Now we will be having 2 right-angled triangles, with the hypotenuse of each measuring 8 units and the other side measuring 4 units

Mathematically to find the altitude, we can solve using Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

Let’s call the altitude h;

8^2 = h^2 + 4^2

64 = h^2 + 16

h^2 = 64-16

h^2 = 48

h= √(48)

h = 4 √3 units

irrational, then, just means all the numbers that aren't rational. every integer is a rational number, since each integer n can be written in the form n/1. however, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

step-by-step explanation:

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92