HELP ME HELP ME GEOMETRY PROBLM!!!

posted by .

In triangle ABC, m<A = 90, m<B=75, and BC = \sqrt{3}. What is the area of ABC? Express your answer as a common fraction.

HELP THIS IS SO HARD HHELP MEE!!! EXplain too please!

  • HELP ME HELP ME GEOMETRY PROBLM!!! -

    You have a right-angled triangle so we can use the formula
    (1/2) base x height

    Since you want the answer as a common fraction, I will assume that you need "exact" values.

    you state that BC = \sqrt{3}
    I will assume that is meant to say √3
    so cos75 =base/√3
    base = √3cos75
    and sin75 = height/√3
    height = √3sin75

    area = (1/2)(√3sin75)(√3cos75)
    = (3/2)sin75cos75)
    (recall sin 2A = 2sinAcosA)
    = (3/2)(2sin75cos75)/2
    = (3/4) sin 150

    sin 150 = sin30 ---- one of the basic identities

    area = (1/3) sin150
    = (3/4)sin30
    = (3/4)(1/2) = 3/8

  • HELP ME HELP ME GEOMETRY PROBLM!!! -

    thanks alot

  • HELP ME HELP ME GEOMETRY PROBLM!!! -

    THANK YOU !!!!!!!

  • HELP ME HELP ME GEOMETRY PROBLM!!! -

    You don't even need trig for this. Reflect B, draw and altitude from B to B'C and solve

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geometry

    Given: X, Y, and Z are the midpoints of the sides of triangle ABC. Find rhe ratio of the area of triangle XYZ to the area of triangle ABC
  2. geometry!!!!!!

    ABC is an isosceles triangle with AB = BC. The circumcircle of ABC has radius 8. Given further that AC is a diameter of the circumcircle, what is the area of triangle ABC?
  3. Geometry

    ABC is a triangle with area equal to 20 . The incircle of triangle ABC has radius equal to 2 and the circumcircle of triangle ABC has radius equal to 6 . If sinA+sinB+sinC=a/b , where a and b are coprime positive integers, what is …
  4. Geometry

    ABC is a right angled triangle with ∠ABC=90∘ and side lengths AB=24 and BC=7. A semicircle is inscribed in ABC, such that the diameter is on AC and it is tangent to AB and BC. If the radius of the semicircle is an improper …
  5. Hard Geometry Problem

    Hi guys. I need a lot of help on this. "Equilateral triangle ABC has centroid G. Triangle A'B'C' is the image of triangle ABC upon a dilation with center G and scale factor -2/3. Let K be the area of the region that is within both …
  6. Geometry

    Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if (triangle) …
  7. sanket study centre

    In triangle ABC p,q,r such that they lie interior of triang ABC and AP=AR and all the three sides of triangle PQR are scalan if area of triangle PQR is 100 then find area of triangle ABC
  8. Geometry

    Triangle $ABC$ is isosceles with point $A$ at the point $(2, 7)$, with point $B$ at $(-2, 0)$ and with point $C$ at $(3, -1).$ Triangle $ABC$ is reflected over $\overline{BC}$ to form $\triangle A'BC$. Triangle $A'BC$ is reflected …
  9. maths

    DRAW LOCUS OF POINT SO THAT IT IS EQUIDISTANT FROM BC & CA . ... constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch ... 16) AB = 3.2cm BC = 8.4cm The area of the triangle ABC …
  10. geometry

    Isosceles $\triangle{ABC}$ has a right angle at $C$. Point $P$ is inside $\triangle{ABC}$, such that $PA=11$, $PB=7$, and $PC=6$. Legs $\overline{AC}$ and $\overline{BC}$ have length $s=\sqrt{a+b\sqrt{2}}$, where $a$ and $b$ are positive …

More Similar Questions