The angles of a triangle are in the ratio 1 : 4 : 5.
Work out the size of the smallest angle?

18°

Step-by-step explanation:

sum the parts of the ratio, 1 + 4 + 5 = 10 parts

The sum of the 3 angles in a triangle = 180° , then

180° ÷ 10 = 18° ← value of 1 part of the ratio

Since 1 is the smallest part of the ratio it represents the smallest angle, thus

smallest angle = 18°

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it