The 30º-60º-90º triangle is a special case you'd do well to remember, because the legs always occur in the same ratio to one another. As your picture shows (I'm guessing "SL" stands for short leg?), the sides labeled 4, y and x occur in a ratio of 1 to √3 to 2.
This means
sin(30º) = SL/(2*SL) = 1/2
tan(30º) = SL/(√3*SL) = 1/√3
(and also cos(30º) = (√3*SL)/(2*SL) = √3/2, though you don't really need that here)
So in this triangle, x and y satisfy
sin(30º) = 4/x
tan(30º) = 4/y
This comes straight from the definitions of sine and tangent. Then
4/x = 1/2 ==> x = 8
4/y = 1/√3 ==> y = 4√3
Angle t would be equal to cos(60 degrees) which has coordinates (1/2,sqrt3/2) so that answer is 1/2
Answer:
8
Step-by-step explanation:
There are 42 people who had breakfast. Each person had either egg or pancake or both.
Of these only eggs were 2/3 and both were 2/3
Hence the remaining ate only pancakes
i.e. portion of persons who ate pancakes = 1-(1/7+2/3)
= 4/21
Total no of people in the restaurant = 42
Of those people who ate eggs only= 1/7 (42) = 6
No of persons who ate both pancakes and eggs = 2/3(42) = 28
Hence no of persons who ate only pancakes =42-(6+28) = 8
