triangle

02 Trapezoidal lot segregated from triangular land

Situation
A triangular lot ABC have side BC = 400 m and angle B = 50°. The lot is to be segregated by a dividing line DE parallel to BC and 150 m long. The area of segment BCDE is 50,977.4 m2.
 

Part 1: Calculate the area of lot ABC.
A. 62,365 m2
B. 59,319 m2
C. 57,254 m2
D. 76.325 m2
 

Part 2: Calculate the area of lot ADE.
A. 8,342 m2
B. 14,475 m2
C. 6,569 m2
D. 11,546 m2
 

Part 3: Calculate the value of angle C
A. 57°
B. 42°
C. 63°
D. 68°
 

715 Semicircle and Triangle | Centroid of Composite Figure

Problem 715
Determine the coordinates of the centroid of the area shown in Fig. P-715 with respect to the given axes.
 

Semicircle surmounted on top of a right triangle

 

Derivation of Heron's / Hero's Formula for Area of Triangle

For a triangle of given three sides, say a, b, and c, the formula for the area is given by
 

$A = \sqrt{s(s - a)(s - b)(s - c)}$

 

where s is the semi perimeter equal to P/2 = (a + b + c)/2.
 

010 Components of force normal and tangent to hypotenuse of a triangle

Problem 010
The triangular block shown in Fig. P-010 is subjected to the loads P = 1600 lb and F = 600 lb. If AB = 8 in. and BC = 6 in., resolve each load into components normal and tangential to AC.
 

Triangular block subjected to two forces

 

40 - Base angle of a growing right triangle

Problem 40
The base of a right triangle grows 2 ft/sec, the altitude grows 4 ft/sec. If the base and altitude are originally 10 ft and 6 ft, respectively, find the time rate of change of the base angle, when the angle is 45°.
 

Trapezoidal Strip of Land from a Triangular Lot

Problem
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.

A. 7.1 m
B. 8.1 m
C. 8.7 m
D. 7.7 m
 

 
 
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