JCSF ENGINEERING REVIEW CENTERMATH 0005MATHEMATICS prepared by: ENGR. CHRISTIAN M. PANGANIBAN TRIGONOMETRY AN SO!I MENS"RATION1. Find the area of the triangle below:a. 46 mPP2PP b. 64 mPP2PP c.80 mPP2PP d. 96 mPP2PPA#$%er: B. &' (PP)PPFormulas:Radius of the Circumscribed Circle about a TriangleBut the given triangle is an isosceles triangle with two e!ual sides and two e!ual angles"#nd also$ the given triangle is a right triangle with one angle e!ual to 90%"&hus$ Area of a Right Triangle$'sing the two formulas$( ) semi*+erimeter a$ b$ c ) three sides of triangle where:a$ b$ c ) three sides of triangle#$ B$ , ) three interior angles p*. +triangle the of sides cb, a, ; triangle the of areaA ; circle of radius r : whereA 4c b ar B tan a21A tan b21ab21Area2 2 2 222222 2 22 22 2m 64 45 tan ) 45 sin 16 (21A orm 64)( 4) 16 ( ) (16sin45 Area !hus,16sin45 b ;16bsin45triangle, rightthe "onsiderm 162#2c ; b21#2c b2, $%uation and 1 $%uation e%uating2 $%uation b21 Area ; 45 tan b21 A tan b21but Area1 $%uation#2c b Area ;)( 4c bArea thus,mr butr 4c bArea or A 4c br) (isosceles b a butA 4abcr : usesides # of lenghtsthe gi&en !'(A)*+$ ,B+(-.$ an but triangle righta notis triangle gi&en the (f : )ote 2c b a/where,)(/0c) /(/0a)(/0b A: 1,'2.+A / 3$',4+ + use:en, le are gi& ludedang their inc sides and 2 But:(f " sin ab21B sin ac21A sin bc21 Area 45 45bacA B"5156rJCSF ENGINEERING REVIEW CENTERMATH 00052. Find the radius of a circle inscribed in a triangle with sides of - cm$ . cm and 10 cm.a. 1.4.. cm b. 2.4.. cm c. /.4..cm d. 4.44. cmA#$%er: A. +.',, -(Formulas:Radius of the Inscribed Circle in a Triangle(ince / sides of triangle are given$ 0ero1s Formula can be used.&hus$ /. &he area of a triangle whose sides are 2- cm$ /9 cm and 40 cm is:a. 468 cmPP2PPb. 648 cmPP2PPc. 846 cmPP2 PP d. 498 cmPP2 PPA#$%er: A. '&. -(PP)'se 0ero1s Formula:PP4. (olve for the length of the h2+otenuse of a right triangle if lengths of the two legs are . m and 16 m$ res+ectivel2.a. 10./6/ m b. 12.-6. mc. 1-.648 m d. 1..464 mA#$%er: . +,.'&' ('se Pythagorean Theorem for 3ight &riangles onl2"&hus$-. #n obli!ue triangle has sides a ) 6 cm$ b ) 9 cm and angle , ) /2%. (olve the other angles of the triangle.a. /9%61484 5 108%-11-44b. /9%61484 5 98%-11-44c. 40% 5 80% d. -0% 5 102% A#$%er: A. /01&2'.3 4 +0.15+25'3Formulas: F5r Ob6789e Tr7a#*6e$&hus$6ote: S9( 5: ; 514 15 15865 6181#5 0 15 or 1#5 8 61 B ;#2 sin54 8 5sinB 4 4 6 #< A ;#2 sin54 8 5sinA6cm 54 8 5 #2 cos ) < )( 6 ( 2 < 6 " cos ab 2 b a c2 2 2 2"BAabcJCSF ENGINEERING REVIEW CENTERMATH 00056. 7iven a triangle with angle , ) 28..%$ side a ) 1/2 units and b ) 224 units. (olve for the angle B.a. 140.94% b. 1/0.94%c. 120.94% d. 80.94% A#$%er: C. +)0.0'1.. &he +erimeter of a smallrectangular industriallot is 140 m and its diagonalis -0 m. Find the area of the lot ins!uare meters.a. 12-0b. 1200 c. 1/00d. 1-00A#$%er: B. +)00Formulas:Perimeter of a Rectangle,

Area of a Rectangle,8. 8f a right circular cone has a base radius of /- cm and an altitude of 4- cm$ solve for the total surface area in cmPP2PPand volume in cmPP/PP$ of the cone.a. 9$8-..6. 5 4-$0/4.44 b. 10$116.89 5 -.$.26... c. 6$268.44 5 -..26... d. none of these A#$%er: B. +0=++&..0 4 5,=,)&.,,Formulas:Lateral Surface Area of a Cone, ABBLSBBArea of the base of a Cone (Area of Circle), ABBBolume of a Cone, &hus$ 9. 8f one of the edges of a cube measures 12 cm. ,alculate the surface area in cmPP2PP$ and the volume in cmPP/PP. p*. / + + + + 1258 +?) 5: ;